1. The probability density of a random variable X is given in the following figure.

The probability that X is at least 0.5 is:

a.0.

b.1/4.

c.1/2.

d.3/4.

1. An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. The conditional probability of B, given A, is:

A.5/6.

b.1/5.

c.1/6.

d.The answer cannot be determined from the information given.

1. A small class has 10 students. Seven of the students are male and three are female. You write the name of each student on a small card. The cards are shuffled thoroughly, and you choose one at random, observe the name of the student, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe the name, and replace it in the set. This is done a total of five times. Let X be the number of cards observed in these five trials with a name corresponding to a male student. The random variable X has which of the following probability distributions?

a.the Normal distribution, with mean 3 and variance 1

b.the binomial distribution, with parameters n = 5 and p = 0.3

c.the binomial distribution, with parameters n = 5 and p = 0.7

d.None of the answer options is correct.