In a box of 7 batteries,6 are dead.You choose two batteries at random from the box.Let the random variable X be the number of good batteries you get.Find the expected value of X.
A)μ = 0.36
B)μ = 0.92
C)μ = 0.14
D)μ = 1.71
E)μ = 0.29

Question

Quizplus · Accepted Answer

The expected value, E(X), of the number of good batteries chosen can be calculated using the formula for expectation: E(X) = Σ [x * P(x)], where x is a value that the random variable can take on and P(x) is the probability of x occurring. There are three scenarios:1. Picking 0 good batteries: The probability is (6C2)/(7C2) = 15/21 = 5/7.2. Picking 1 good battery: The probability is (6C1)*(1C1)/(7C2) = 6/21 = 2/7.3. Picking 2 good batteries: The probability is (1C2)/(7C2) = 0 (since you can't pick 2 good batteries out of 1).Thus, E(X) = (0 * 5/7) + (1 * 2/7) + (2 * 0) = 0 + 2/7 + 0 = 2/7 ≈ 0.29.

In a Box of 7 Batteries,6 Are Dead