Learning Objectives

# Problem 1 of 3

A biased (weighted) coin is designed so that the probability of a head on each flip is (3/5).

(a) If this biased coin is flipped 3 times, what is the probability that the first 2 flips are tails and the third flip is a head?

(b) If this biased coin is flipped until exactly 2 heads appear, what is the probability that it takes exactly 3 flips until the second head appears?

(c) If this biased coin is flipped 7 times, what is the probability that exactly 3 or 4 heads appear?

**Solution**

# Problem 2 of 3

It is known that 10% of a population has a certain disease. For a patient without the disease, a blood test for the disease gives a correct diagnosis 95% of the time. For a patient with the disease, the test gives a correct diagnosis 99% of the time. What is the probability that a person whose blood test shows the disease actually has the disease?

**Solution**

# Problem 3 of 3

There are 35 students in a room; 18 of the students are girls and 17 are boys. Three students are chosen at random for a committee.

(a) What is the probability that **exactly** 2 of the students are girls?

(b) What is the probability that **at least** 2 of the students are girls?

**Solution**

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