Question

Please help with this question? im confused!
You have 15 red checkers and 5 black checkers. Checkers are selected one at a time with replacement. Each time you record the checker color that is selected. Find the probability of selecting a red checker exactly 4 times in 10 selections.

Answer 1

binomial probability for this one

Answer 2

the probability of selecting a red checker on any one pick is \(\frac{15}{20}=\frac{3}{4}\) and the probability of selecting a black one is \(\frac{1}{4}\)
you want exactly 4 red in 10 selections

Answer 3

see I don't understand that. That's why im confused on it.
Would it start off with 10c^7?

Answer 4

i can explain but it will take a second

Answer 5

i assume you mean \(_{10}C_4\) right?

Answer 6

yeah

Answer 7

first off, do you get the \(\frac{3}{4}\) part, and the \(\frac{1}{4}\) part?

Answer 8

Is that the 4 times you could select a red checker outta the 10?

Answer 9

no

Answer 10

that is the probability you get a red checker

Answer 11

the ratio of the red checkers to the total number of checkers is \(\frac{15}{20}=\frac{3}{4}\) so the probability you get a red checker on any ONE pick is \(\frac{3}{4}\) and the probability you get a black one is \(\frac{1}{4}\)

Answer 12

so the beginning of it would look like
10C4 * (3/4)^7 * (1/4)^3

Answer 13

except that you want 4 red and 6 black

Answer 14

so it would be
\[\large _{10}C_4\left(\frac{3}{4}\right)^{\color{red}4}\left(\frac{1}{4}\right)^6\]