Question

Consider a binomial experiment with two trials and p = .4. SHOW YOUR WORK!

List all of the possible outcomes for the two trials. (2 points)

Compute the probability of one success, P(1). (1 point)

Compute P(0). (1 point)

Compute P(2). (1 point)

Find the probability of at least one success P(x ? 1). (2 points)

Find the expected value. (1 point)

Find the variance. (1 point)

Answer 1

We have p = 0.4

1. We know that P(1) = 2C1*p¹*(1 – p)¹

= 2 * 0.4 * 0.6 = 0.48

2. We know that P(0) = (1 – p)²

= 0.6² = 0.36

3. We know that P(2) = (p)²

= 0.4² = 0.16

4. Probability of at least one success P(x, 1) = 1 – P(0)

= 1 – 0.36 = 0.64

5. Expected value = n*p = 2*0.4 = 0.8

                                                    = 0.80

6. Variance = n*p*(1-p)

    = 2 * 0.4 * 0.6 = 0.48