Probability Test Review

Given U={1,2,3,4,5,6,7,8,9}; A={2,4,6,7,8}; B={1,3,5,7}.

What is A ∩ B?

• {1,2,3,4,5,6,7,8}

• {9}

• {7}

• does not have an intersection

Answer explanation

In common between set A and set B

What is the probability that a randomly selected student prefers basketball given that the student is female?

• 15/31

• 15/48

• 16/52

• 16/31

Answer explanation

"given that the student is female" is the subgroup, so then 52 is the denominator. Of those 52 females, 16 prefer basketball.

Consider the events: X-The selected student is male. Y-The student prefers football. Select the true statement.

• The events are independent because the number of categories for sports preference is different from the number of categories for gender.

• The events are independent because the number of male students is greater than the number of students who prefer football.

• The events are dependent because for the preferred sports the males like football the most.

• The events are dependent because the probability of X is not equal to the probability of X given Y.

Answer explanation

P(males and football) does not equal P(males)*P(football)

Based on the results of a survey, which of the following statement ARE TRUE?

• A total of 140 students were surveyed

• More students speak a foreign language

• More than 50% of the students surveyed speak a foreign language

• Less than 50% of the students who speak a foreign language have an average of greater than 90 in math

Answer explanation

Find totals and check each multiple choice answer - tip

When looking at the association between the events "owns a home" and "owns a PS5," if the events are independent, then the probability P(owns a home | owns a PS5) is equal to which of the following?

• P(owns a home)

• P(owns a PS5)

• P(owns a home) * P(owns a PS5)

• P(owns a home) + P(owns a PS5)

Events A and B have probabilities such that P(A)=0.6, P(B)=0.42, P(A∪B)=0.56, and P(A∩B)=0.24. Are events A and B independent?

• No, because P (A) - P (B) = P (A ∩ B)

• No, because P (A) * P (B) = P (A ∩ B)

• Yes, because P (A) + P (B) = P (A ∩ B)

• Yes, because P (A) + P (B) = P (A ∩ B)

How many students like dogs and birds, but not cats?

• 1

• 4

• 12

• 2

In negotiations between the BOE, it is estimated that there is a 60% chance that an agreement will be reached on the salaries of the teachers. It is estimated that there is a 30% chance that there will be an agreement on the insurance benefits. There is a 15% chance that no agreement will be reached on either issue. What is the probability that an agreement will be reached on both issues

• 85%

• 90%

• 18%

• 5%

Answer explanation

85=90+30-P(both) and you are solving for P(both)

The STEM Academy has reported that of the Sophomore class, 5.8% are in Band, D, 25% are enrolled in Geometry, G, and 3.9% are in both. What is the probability of students enrolled in Geometry(G) given the students are in Band(B)?

• 67%

• 1%

• 23%

• 49%

240 students are taking science classes. There are 104 people studying chemistry and 132 people studying biology. Half of the students studying chemistry take biology. What is the probability that a person is studying chemistry OR is studying biology?

• 52/132

• 52/240

• 184/240

• 236/240