Question

has removed two dead batteries from a flashlight and inadvertently mingled themwith the two good batteries he intended as replacements. The four batteries look identical. Elon now randomly selects two of the four batteries. What is the probability he selects the two good batteries

Answer 1

Using the hypergeometric distribution, it is found that there is a 0.1667 = 16.67% probability that he selects the two good batteries.

The batteries are chosen from the sample without replacement, which is why the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.
• N is the size of the population.
• n is the size of the sample.
• k is the total number of desired outcomes.

In this problem:

• There are 4 batteries, thus $N = 4$.
• Sample of 2 batteries, thus $n = 2$
• 2 are good, thus $k = 2$.

The probability that both are good is P(X = 2), thus:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,4,2,2) = \frac{C_{2,2}C_{2,0}}{C_{4,2}} = 0.1667$

0.1667 = 16.67% probability that he selects the two good batteries.

A similar problem is given at https://brainly.com/question/24826394