There are 12 red checkers and 3 black checkers in a bag. Checkers are selected one at a time, with replacement. Each time, the color of the checker is recorded. Find the probability of selecting a red check exactly 7 times in 10 selections.

Question

kropot72 · Answer

This can be solved by using the binomial distribution. Have you studied this distribution?

anonymous · Answer

Not really no

kropot72 · Answer

The calculation using the binomial distribution is as follows:
$$P(red\ 7\ out\ of\ 10)=\left(\begin{matrix}10 \ 7\end{matrix}\right) \times (0.8)^{7} \times(0.2)^{3}=\frac{10\times9\times8}{3\times2}\times(0.8)^{7}\times(0.2)^{3}$$

kropot72 · Answer

So we can simplify the calculation to:$$120\times(0.8)^{7} \times(0.2)^{3}=you\ can\ calculate$$

anonymous · Answer

Alright, after using a calculator I got= 
0.201326592

kropot72 · Answer

Good work! You are correct. Now you just need to round your answer to the required number of decimal places, if required.

anonymous · Answer

It does not specify, but thank you very much!

kropot72 · Answer

You're welcome :)