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PERRERAS, Karen A. (Activity 6)

This document contains the work of a student named Karen A. Perreras. It includes solutions to 3 probability problems involving conditional probability: 1) Finding the probability of various outcomes when rolling a pair of dice. 2) Finding probabilities related to drawing cards from a standard deck. 3) Calculating probabilities based on a survey of children's preferences for a zoo animal. The problems involve finding conditional probabilities such as the probability a child selected tiger given they are a girl.

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37 views3 pages

PERRERAS, Karen A. (Activity 6)

This document contains the work of a student named Karen A. Perreras. It includes solutions to 3 probability problems involving conditional probability: 1) Finding the probability of various outcomes when rolling a pair of dice. 2) Finding probabilities related to drawing cards from a standard deck. 3) Calculating probabilities based on a survey of children's preferences for a zoo animal. The problems involve finding conditional probabilities such as the probability a child selected tiger given they are a girl.

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karen perreras
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Name: _Karen A.

Perreras_

Section: III-AMA____________

Activity 6
Conditional Probability of an Event
I. Solve the following problem sets and make sure to show your solution.

1. A pair of dice is rolled, and the sum of the dice is recorded, determine the probability
that:

a. the sum is greater than 9 given the second dice is a 6.

A= {(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
B= {(6, 4), (6, 5), (6, 6)}

P (A) = 6
P (B) = 3

P ( BA )= 36 = 12
b. the sum is odd given the first dice is a 3.

A = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)}
B = {(3, 2), (3, 4), (3, 6)}

P (A) = 6
P (B) = 3

P ( BA )= 36 = 12
c. a double is not rolled given the sum is greater than 10.

A = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2),
(3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,2), (5,2), (5,3), (5,4), (5,5),
(5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

B= {(5, 6), (6, 5), (6, 6)}

P (A) = 36
P (B) = 3
P ( )
B 3
= =
1
A 36 1 2

2. One card is selected from a deck of cards find the probability that:
a. the card is a queen given that it is a face card.
P (A) = 12
P (B) = 4

P ( BA )= 124 = 13
b. the card is not a seven given it is between 3 and 8 inclusive.
P (A) = 24
P (B) = 20

P ( BA )= 2420 = 56
c. the card is not red given it is a queen.
P (A) = 4
P (B) = 2

P ( BA )= 24 = 12
3. At a zoo, a sampling of children was asked if the zoo were to get one additional animal,
would they prefer a tiger or a giraffe. The results of the survey follow:

Respondents Tiger Giraffe Total


Boys 90 110 200
Girls 75 85 160
Total 165 195 360

If one child who was in the survey is selected at random, find the probability that:

a. the child selected the tiger, given the child is a girl.


P (A) = 165
P (B) = 75

P ( BA )= 165
75
=
5
11

b. the child is a boy, given the child preferred the giraffe.


P (A) = 200
P (B) = 110

P ( BA )= 110 =
200 20
11

c. the child selected is a girl, given that the child preferred the tiger
P (A) = 160
P (B) = 75

P ( BA )= 160
75 15
=
32

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