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7th - More practice with Probability

Last updated over 2 years ago
22 questions
Rachel and her little sister Christie often argue about who should wash the dishes at their house.  Rachel suggests that they flip coins to solve their argument.

"Flipping a coin is fair, since heads and tails each have an equal chance of happening.  Each one has a probability of 1/2,” Rachel says.  “If the coin shows heads, then I do the dishes.  If it shows tails, then you do them.”
1

Is this system fair? 
That is, does each girl have an equal likelihood of washing the dishes each day? 
What is the theoretical probability for heads?  For tails?

Explain your reasoning

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Rachel and Christie flip a coin every evening for the first week. 
Christie has washed the dishes four times, and Rachel has washed the dishes three times. 
Christie tells Rachel that the system is not fair, because Christie has done the dishes more often than Rachel. 
Is Christie right?

Explain your reasoning

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After the second week of coin flipping, Christie has washed the dishes ten times and Rachel has washed the dishes four times. 
Now Christie is really upset at Rachel because she has washed the dishes so many times.

In light of this new information, do you think the system is fair or not fair? 
What would you recommend to Christie? 

Discuss your ideas with your team. Explain your reasoning here

1

Can you find a theoretical probability for:

Picking an Ace from a standard 52-card deck.

If you can find it, state the theoretical probability

1

Can you find a theoretical probability for:

Not rolling a 3 on a standard number cube.

If you can find it, state the theoretical probability

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Can you find a theoretical probability for:

The chances of a thumbtack landing with its point up or on its side.

If you can find it, state the theoretical probability

1

Can you find a theoretical probability for:

Getting the one red crayon from a set of eight different-color crayons.

If you can find it, state the theoretical probability

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Is this more than, less than, or equal to 50%, the theoretical probability of flipping heads?

So far in this section, you have worked with probabilities involving one specific desired outcome. 
Now you will investigate probabilities of compound events. 
Compound events are events with combinations of outcomes. 

You will find the probability that either one of the events or the other event occurs.
Ms. Chin lets her students borrow pens and pencils on days when they have a quiz. 
She has a paper bag containing hundreds of wooden pencils, mechanical pencils, and blue pens.

Mathias forgot his pencil, and it is quiz day! 

Ms. Chin tells him that one out of every three students who reaches into the bag pulls out a wooden pencil.  Two out of every five students pull out a mechanical pencil. 
The rest of the students pull out a blue pen.
1

If Mathias reaches into the bag without looking, is it more likely that he will choose a wooden pencil or a mechanical pencil?  Explain your thinking

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How can you describe the probability that Mathias will pull out some kind of pencil—either a wooden pencil or a mechanical pencil—by using the probabilities that you already know? 

Consider what you know about adding and subtracting fractions and see if you already have a strategy to write this probability as a single number.

1

William shuffles a standard deck of 52 playing cards and starts to turn them over one at a time. 
The first three cards he turns over are an ace, a 4, and a jack.

How many cards are left in the deck?

1

William shuffles a standard deck of 52 playing cards and starts to turn them over one at a time. 
The first three cards he turns over are an ace, a 4, and a jack.

How many of the remaining cards are aces?

1

William shuffles a standard deck of 52 playing cards and starts to turn them over one at a time. 
The first three cards he turns over are an ace, a 4, and a jack.

What is the probability that the fourth card will be an ace?

1

William shuffles a standard deck of 52 playing cards and starts to turn them over one at a time. 
The first three cards he turns over are an ace, a 4, and a jack.

Instead of getting an ace, he gets a 2 as the fourth card.
The fifth card is a 5. 

What is the probability that the next card will be a king?

1

Lindsay has a paper bag full of Fruiti Tutti Chews in three different fruit flavors. 
She says, “If you reach into the bag, you have a 1/3 chance of pulling out a Killer Kiwi.  There is a 3/5 chance that you will get Crazy Coconut.”

If you reach into the bag, what is P(coconut or kiwi)?

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Does there have to be another flavor in the bag? 
How can you tell? 
If so, assuming that there is only one other flavor, what is the probability of getting that flavor?

1

How many candies might Lindsay have in the bag?  Is there more than one possibility?

In a power outage, Rona has to reach into her closet in the dark to get dressed. 
She is going to find one shirt and one pair of pants. 
She has three different pairs of pants hanging there: one black, one brown, and one plaid. 
She also has two different shirts: one white and one polka dot.

Draw a probability tree to organize the different outfit combinations Rona might choose in your notebook
1

What is the probability that she will wear both a polka dot shirt and plaid pants?

1

What is the probability that she will not wear the black pants?

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Make a probability table for Rona’s outfits in your notebook.
Which way of representing the outcomes do you like better?

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Are the events polka dot and plaid mutually exclusive? Explain

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Are the events polka dot and white mutually exclusive?  Explain