Lesson 5.3 Binomial Situations & Binomial Probability Practice Due 2/1 PM

Remember: for a situation to be considered a Binomial Situation it needs to qualify:
B- There are only two possible outcomes for each trial (Success or Failure)
I- Trials are independent.
N-  Set number of trials, known in advance
S- probability of success, 'p' , is the same for each trial. This is known in advance.

Required

3

Is the following situation a Binomial Situation? Think through the four criteria above.
If not, why not?
We roll 50 dice to find the distribution of the number that is rolled.
X= the number rolled by a dice
Success= not given

Choose the three answers that apply to this situation.

Required

4

Is the following situation a Binomial Situation? Think through the four criteria above.
If not, why not?
How likely is it that in a group of 120 people, the majority may have Type A blood, given that 43% of the population have type A.
Trial = person's blood type
Success= having type A blood
Failure= not having type A blood

Choose the four answers that apply to this situation.

Required

3

Is the following situation a Binomial Situation? Think through the four criteria above.
If not, why not?
We deal 7 cards from a well shuffled deck of cards (do not replace them) and get all hearts. How likely is that?
Trial = how many hearts out of 7 cards dealt
Success= card that is a heart
Failure= card that is not a heart

Choose the three answers that apply to this situation.

Required

3

Is the following situation a Binomial Situation. Think through the four criteria above.
If not, why not?
You are rolling 5 dice and need to get at least two 6's to win the game.
Trial = rolling 5 dice
Success= roll a 6
Failure= do not roll a 6
B- 2 possible outcomes, I-independent events, N-number of trials, S-set probability
Choose the three answers that apply to this situation.

Required

3

Is the following situation a Binomial Situation?
Think through the four criteria above.
If not, why not?
We record the distribution of eye colors in a group of people (brown, blue, green, hazel, other).
Trial = eye color of each person
Success= Blue, Brown or Green eyes
Failure= not clear

Choose the three answers that apply to this situation.

Required

4

Use the Binomial Probability Equation:
An Olympic archer is able to hit the bull’s-eye 80% of the time.
Assume each shot is independent of the others.

If she shoots 6 arrows, what is the value of 'n'?

Required

4

Use the Binomial Probability Equation:
An Olympic archer is able to hit the bull’s-eye 80% of the time.
Assume each shot is independent of the others.

If she shoots 6 arrows, what is the value of 'p'? (probability of success, hitting the bull's-eye)
Enter your answer as a decimal.

Required

4

Use the Binomial Probability Equation:
An Olympic archer is able to hit the bull’s-eye 80% of the time.
Assume each shot is independent of the others.
If she shoots 6 arrows, what is the value of '1-p' (also known as q )?
(probability of failure, not hitting the bull's-eye)

Required

4

Use the Binomial Probability Equation:
An Olympic archer is able to hit the bull’s-eye 80% of the time.
Assume each shot is independent of the others.

Use the formula:
If she shoots 6 arrows, what is the probability that she gets exactly 4 Bull’s-eyes?
P(X=4):
Use the TI-Nspire to find your answer.
Enter your answer as a decimal rounded to three places past the decimal point.

Required

4

An Olympic archer is able to hit the bull’s-eye 80% of the tme.
Assume each shot is independent of the others.

Use the formula:
If she shoots 6 arrows, what is the probability that she gets exactly 5 Bull’s-eyes?
P(X=5):
Enter your answer as a decimal rounded to three places past the decimal point.

Required

4

An Olympic archer is able to hit the bull’s-eye 80% of the tme.
Assume each shot is independent of the others.

Use the formula:

If she shoots 6 arrows, what is the probability that she gets all 6 Bull’s-eyes?
P(X=6):
Enter your answer as a decimal rounded to three places past the decimal point.

Required

4

Using the information from the previous three questions, what is the probability that the Olympic Archer is able to hit the bull's-eye at least four times out of 6 shots?

Hint: P(at least 4 bull’s-eyes)= P(4 bull's-eyes) or P(5 bull's-eyes) or P(6 bull's-eyes)

Required

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.
Assuming the shots are independent, what's the value of 'n'?

Required

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.
Assuming the shots are independent, what's the value of 'p'? (probability of success, making the basket)
Enter your answer as a decimal.

Required

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.
Assuming the shots are independent, what's the value of '1-p' (or q)?
(probability of failure, not making the basket)
Enter your answer as a decimal.

Required

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.

Now that you have identified n, p, q, use the formula:

Assuming the shots are independent, what's the probability he makes exactly 3 of the 5 shots?
Enter your answer as a decimal rounded to three places.

Required

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.

Now that you have identified n, p, q, use the formula:

Assuming the shots are independent, what's the probability he makes exactly 4 of the 5 shots?
Enter your answer as a decimal rounded to three places.

Required

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.

Now that you have identified n, p, q, use the formula:

Assuming the shots are independent, what's the probability he makes all 5 of the 5 shots?
Enter your answer as a decimal rounded to three places.

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.

Use the answers to the previous three questions: what's the probability he makes at least three of the 5 shots?
Enter your answer as a decimal rounded to three places.

Required

4

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.

Use the answers to the previous question: what's the probability he makes less than three of the 5 shots?
Enter your answer as a decimal rounded to three places.
Hint: At least three shots has a complement, what is the opposite of making at least 3?
Use the fact that complements need to add to 1.0 to find your probability for less than three shots.

Remember: for a situation to be considered a Binomial Situation it needs to qualify:

B- There are only two possible outcomes for each trial (Success or Failure)

I- Trials are independent.

N- Set number of trials, known in advance

S- probability of success, 'p' , is the same for each trial. This is known in advance.

Is the following situation a Binomial Situation? Think through the four criteria above.If not, why not?We roll 50 dice to find the distribution of the number that is rolled.X= the number rolled by a diceSuccess= not givenChoose the three answers that apply to this situation.

Use the Binomial Probability Equation:An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what is the value of 'n'?

Use the Binomial Probability Equation:An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what is the value of 'p'? (probability of success, hitting the bull's-eye)Enter your answer as a decimal.

Use the Binomial Probability Equation:An Olympic archer is able to hit the bull’s-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what is the value of '1-p' (also known as q )? (probability of failure, not hitting the bull's-eye)

An Olympic archer is able to hit the bull’s-eye 80% of the tme. Assume each shot is independent of the others. Use the formula:If she shoots 6 arrows, what is the probability that she gets all 6 Bull’s-eyes? P(X=6):Enter your answer as a decimal rounded to three places past the decimal point.

Using the information from the previous three questions, what is the probability that the Olympic Archer is able to hit the bull's-eye at least four times out of 6 shots?Hint: P(at least 4 bull’s-eyes)= P(4 bull's-eyes) or P(5 bull's-eyes) or P(6 bull's-eyes)

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.Assuming the shots are independent, what's the value of 'n'?

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.Assuming the shots are independent, what's the value of 'p'? (probability of success, making the basket)Enter your answer as a decimal.

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game. Assuming the shots are independent, what's the value of '1-p' (or q)? (probability of failure, not making the basket)Enter your answer as a decimal.

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game. Use the answers to the previous three questions: what's the probability he makes at least three of the 5 shots?Enter your answer as a decimal rounded to three places.

Is the following situation a Binomial Situation? Think through the four criteria above.
If not, why not?
We roll 50 dice to find the distribution of the number that is rolled.
X= the number rolled by a dice
Success= not given

Choose the three answers that apply to this situation.

Use the Binomial Probability Equation:
An Olympic archer is able to hit the bull’s-eye 80% of the time.
Assume each shot is independent of the others.

If she shoots 6 arrows, what is the value of 'n'?

Use the Binomial Probability Equation:
An Olympic archer is able to hit the bull’s-eye 80% of the time.
Assume each shot is independent of the others.

If she shoots 6 arrows, what is the value of 'p'? (probability of success, hitting the bull's-eye)
Enter your answer as a decimal.

Use the Binomial Probability Equation:
An Olympic archer is able to hit the bull’s-eye 80% of the time.
Assume each shot is independent of the others.
If she shoots 6 arrows, what is the value of '1-p' (also known as q )?
(probability of failure, not hitting the bull's-eye)

Using the information from the previous three questions, what is the probability that the Olympic Archer is able to hit the bull's-eye at least four times out of 6 shots?

Hint: P(at least 4 bull’s-eyes)= P(4 bull's-eyes) or P(5 bull's-eyes) or P(6 bull's-eyes)

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.
Assuming the shots are independent, what's the value of 'n'?

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.
Assuming the shots are independent, what's the value of 'p'? (probability of success, making the basket)
Enter your answer as a decimal.

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.
Assuming the shots are independent, what's the value of '1-p' (or q)?
(probability of failure, not making the basket)
Enter your answer as a decimal.

A basketball player, who has made 70% of his foul shots during the season, gets to take 5 shots in the first playoff game.

Use the answers to the previous three questions: what's the probability he makes at least three of the 5 shots?
Enter your answer as a decimal rounded to three places.