Question

The batteries to the remote control for your television have just run out. you find your collection of miscellaneous "AA" batteries and grab 2 of them to replace the used ones. The box you used to fish out the replacements contained 14 batteries, but you were unaware that 5 of them were faulty and did not work.

if the remote control requires two good batteries to operate properly, what is the probability that the remote control now works properly?

Answer 1

Answer on Question #60240 – Math – Statistics and Probability

Question

The batteries to the remote control for your television have just run out. You find your collection of miscellaneous "AA" batteries and grab 2 of them to replace the used ones. The box you used to fish out the replacements contained 14 batteries, but you were unaware that 5 of them were faulty and did not work.

if the remote control requires two good batteries to operate properly, what is the probability that the remote control now works properly?

Solution.

The set of elementary events is

$$\Omega = \{(B, B) | B \text{ is one of 14 batteries}\},$$

hence

$$|\Omega| = C_{14}^2,$$ $$A = \{(B, B) | B \text{ is one of that good batteries}\},$$

thus

$$|A| = C_9^2,$$

due to classical definition of probability

$$P(A) = \frac{|A|}{|\Omega|} = \frac{\frac{9!}{2!7!}}{\frac{14!}{2!12!}} = \frac{36}{55} \approx 65.45\%.$$

Answer: $\frac{36}{55}$.

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