AP Statistics 4.5 Conditional Probability- MCQs - Exam Style Questions

Question

The staff at a large farm collected data on the species and sex of animals that they sold last year. The data are displayed in the table.

Animals Sold Last Year

	Male	Female	Total
Horses	17	28	45
Cattle	23	54	77
Total	40	82	122

One of the animals sold last year from the farm will be selected at random. Which of the following is closest to the probability that the animal selected is male given that the animal is a horse?

(A) \(0.139\)
(B) \(0.328\)
(C) \(0.378\)
(D) \(0.425\)
(E) \(0.622\)

▶️ Answer/Explanation

Detailed solution

We want \(P(\text{male}\mid \text{horse})\).
Condition on “horse”: denominator is the total number of horses \(=45\).
Numerator is number of male horses \(=17\).
So \(P(\text{male}\mid \text{horse})=\dfrac{17}{45}\approx 0.378\).
✅ Answer: (C)

Question

In a certain restaurant, 70 percent of the customers order a drink other than water and 44 percent of the customers order dessert. Of the customers who order a drink other than water, 58 percent order dessert.

If one customer from the restaurant is selected at random, which of the following is closest to the probability that the customer ordered a drink other than water and did not order dessert?

(A) 0.034
(B) 0.266
(C) 0.294
(D) 0.406
(E) 0.560

▶️ Answer/Explanation

Let \(D\) = “orders a drink other than water” and \(S\) = “orders dessert.”
We want \(P(D \text{ and } S^c)=P(D)\,P(S^c\mid D)\).
Given \(P(D)=0.70\). Also \(P(S\mid D)=0.58\Rightarrow P(S^c\mid D)=1-0.58=0.42\).
Multiply: \(P(D \text{ and } S^c)=0.70\times 0.42=0.294\).
✅ Answer: (C) 0.294

AP Statistics 4.5 Conditional Probability- MCQs - Exam Style Questions

Question

Question

Resources

Members

Company