Question

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 checker exactly 7 times in 10 selections. Show your work.

Answer 1

I will use the binomial distrubion to find the probability.

`\displaystyle P(A)=\binom{n}{k}p^k(1-p)^(n-k)`

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A - selecting a red checker exactly 7 times in 10 selections

`n=7\\ k=10`

`\displaystyle P(A)=\binom{10}{7}\cdot\left((12)/(15)\right)^7\cdot\left(1-(12)/(15)\right)^(10-7)\\\\ P(A)=(10!)/(7!3!)\cdot\left((4)/(5)\right)^7\cdot\left(1-(4)/(5)\right)^3\\\\ P(A)=(8\cdot9\cdot10)/(2\cdot3)\cdot(16384)/(78125)\cdot\left((1)/(5)\right)^3\\\\ P(A)=120\cdot(16384)/(78125)\cdot(1)/(125)\\\\ P(A)=(393216)/(1953125)\approx0.2=20\%`