# Conditional Probability as Fraction of Outcomes

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## Conditional Probability as Fraction of Outcomes Answer Key

1.

Emily orders two cheese pizzas from Toni's Pizza for herself and some friends. However, Toni's Pizza accidentally put some sausage on a few of the slices of each pizza (shown in the pictures as the shaded slices). The sausage is not visible when just looking at the slice of pizza. Given that one of Emily's friends grabs the pizza containing the three slices of sausage, leaving only the other pizza for Emily to choose from, what is the probability that Emily chooses a slice of sausage pizza?

- 1/4
- 3/8
- 5/16
- 6/16

2.

Peter is dividing a regular deck of 52 cards in half and choosing a card at random. What is the probability of choosing a Jack, if he happens to divide the deck perfectly into black cards and red cards and then chooses from the red cards?

- 1/13
- 2/13
- 1/2
- 1/4

3.

An integer is randomly chosen from the following number line. Given that the number lies on [math]bar{AD}[/math], what is the probability that it also lies on [math]bar{BC}[/math]?

- 1/3
- 2/9
- 1/9
- 1/4

4.

An integer is randomly chosen from the following number line. Given that the number lies on [math]bar{AD}[/math], what is the probability that it also lies on [math]bar{CF} ?[/math]

- 8/8
- 1/2
- 8/11
- 5/8

5.

An integer is randomly chosen from the following number line. Given that the number lies on [math]bar{BE}[/math], what is the probability that it also lies on [math]bar{AF} ?[/math]

- 7/11
- 2/11
- 1
- 4/11

6.

Jane has a collection of marbles, consisting of 3 red, 4 green, 4 blue, and 3 orange marbles. She has offered two of her friends, David and Malcolm, that they may take one marble each. What is the probability that Malcolm chooses a red marble, given that David has already chosen a red marble?

- 1/7
- 2/13
- 3/14
- 1/4

7.

Given the following set of numbers, [math]{1,2,3,4,5,6,7,8,9,10}[/math], what is the probability of choosing an even number, given that a multiple of 3 is chosen?

- 1/2
- 1/3
- 0
- 3/4

8.

Given the following set of numbers, [math]{1,1,1,1,2,3,4,5,5,5,5,6,7,8,8,8,8,8,9,10}[/math], what is the probability of choosing a prime number, given that a factor of 36 is chosen?

- 7/20
- 2/5
- 1/3
- 2/9

9.

Janet, Cam, and Mike arrive at a school party and there are only four cupcakes left. Everyone else has eaten enough cupcakes and will eat no more. Below is table of all possible ways these four cupcakes could be eaten by these three people. How likely it is that Janet will eat more cupcakes than Cam and Mike, given that before Janet gets to the cupcake table, Cam and Mike have already each eaten a cupcake?

[math] "Janet" [/math] | [math] "Cam"[/math] | [math] "Mike" [/math] |

[math] 4 [/math] | [math] 0 [/math] | [math] 0 [/math] |

[math]3[/math] | [math] 1[/math] | [math]0 [/math] |

[math]3[/math] | [math]0 [/math] | [math]1[/math] |

[math]2[/math] | [math]2 [/math] | [math]0[/math] |

[math]2[/math] | [math]0 [/math] | [math]2[/math] |

[math]2[/math] | [math]1 [/math] | [math]1[/math] |

[math]1[/math] | [math]3 [/math] | [math]0[/math] |

[math]1[/math] | [math]0 [/math] | [math]3[/math] |

[math]1[/math] | [math]2 [/math] | [math]1[/math] |

[math]1[/math] | [math]1 [/math] | [math]2[/math] |

[math]0[/math] | [math]4 [/math] | [math]0[/math] |

[math]0[/math] | [math]0 [/math] | [math]4[/math] |

[math]0[/math] | [math]3 [/math] | [math]1[/math] |

[math]0[/math] | [math]1 [/math] | [math]3[/math] |

[math]0[/math] | [math]2 [/math] | [math]2[/math] |

- 4/15, because there are only four possible scenarios in which Janet eats more cupcakes out of the total 15 possibilities.
- 3/14, since for row 1, neither Cam nor Mike has had a cupcake.
- 1/12, because rows 1-3 don't count, as they have Mike and Cam eating only one cupcake between them (and two need to have been already eaten).
- 1/6, since rows 1-5, 7, 8, 11, 12 aren't included as they don't have Cam and Mike as having eaten at least one cupcake each.

10.

Mia goes to East York Collegiate Institute. She is given the following information:

There are 150 grade 12 students at East York Collegiate Institute.

70 of the grade 12 students drive a car at the school.

Half of all students with a grade average of 90 or higher have a car.

She is asked to find the probability of randomly choosing a grade 12 student with a car, given that the student has an average grade of 90 or higher. She reasons initially that, since there are 70 grade 12 students out of 150 who have a car, it would be 7/15. However, since it is a conditional probability, she needs to multiply by 1/2, since the probability that a student with a grade average of 90 or higher is 1/2. This results in a probability of 7/30. Is she correct or not, and why?

There are 150 grade 12 students at East York Collegiate Institute.

70 of the grade 12 students drive a car at the school.

Half of all students with a grade average of 90 or higher have a car.

She is asked to find the probability of randomly choosing a grade 12 student with a car, given that the student has an average grade of 90 or higher. She reasons initially that, since there are 70 grade 12 students out of 150 who have a car, it would be 7/15. However, since it is a conditional probability, she needs to multiply by 1/2, since the probability that a student with a grade average of 90 or higher is 1/2. This results in a probability of 7/30. Is she correct or not, and why?

- Yes, and her reasoning is correct.
- No, she didn't need to multiply by 1/2 and the probability is 7/15. The probability that a student has a car can be assumed to be independent of their grade average, and so no multiplication is needed.
- No, there is insufficient information to find this probability.
- No, she needs to state that it can be assumed that half of grade 12 students have an average of 90 or higher. Therefore, half of 70 is 35, half of 150 is 75, and the probability is 7/15.

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