In a box of 7 batteries,3 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 probability model for X.

Question

Quizplus · Accepted Answer

Let's list out all the possible outcomes when we choose two batteries:
- Good, Good
- Good, Dead
- Dead, Good
- Dead, Dead

Out of these four outcomes, we only care about the first three since they will result in at least one good battery. We can calculate the probability of each outcome as follows:

- Good, Good: (4/7) * (3/6) = 2/7
- Good, Dead: (4/7) * (3/6) = 2/7
- Dead, Good: (3/7) * (4/6) = 2/7

Notice that the probabilities for the first three outcomes are all the same. This means that our probability model for X is:

X = 0 with probability 1/7
X = 1 with probability 4/7
X = 2 with probability 2/7

Therefore, the best choice is B.

In a Box of 7 Batteries,3 Are Dead