Question

Question #5ac9e

Answer 1

`1/11` (without replacement) and `1/9` (with replacement)

Explanation:

1) without replacement:

`(4/12)(3/11) = 12/(11*12) = 1/11`

2) with replacement:

`(4/12)^2 = (1/3)^2 = 1/9`

Explanation :
`4/12` because there are `4` yellow balls out of `4+8 = 12` total balls so the odds of picking a yellow one is `(4/12) = 1/3`
.
If the ball is replaced, the second time we have the same probability `4/12` of picking a yellow one.

However if the ball is not replaced, there are only `3` yellow balls left out of a total of `11` balls, from there `3/11`.

Answer 2

Without replacement: `P(YY)=1/11`

With replacement: `P(YY) = 1/9`

Explanation:

`"Probability" = ("number of desirable outcomes")/("total number of possible outcomes")`

To have BOTH balls yellow means we want to find:

`P(Y Y)" larr` the first ball is yellow AND the second ball is yellow.

For the first ball: `P(Y) = 4/12" "(larr4 " yellow balls")/(larr 12 " balls altogether")`

If the ball is NOT replaced, there is one less yellow ball and one less ball.
For the second ball: `P(Y) = 3/11 " "(larr3 " yellow balls")/(larr 11 " balls altogether")`

`P(YY) = 4/12xx3/11 = 1/11" "larr` (AND implies multiply)

If the first ball IS replaced, the probability stays the same for the second ball being yellow.

For the second ball: `P(Y) = 4/12" "(larr4 " yellow balls")/(larr 12 " balls altogether")`

`P(YY) = 4/12xx4/12 = 16/144 =1/9" "larr` (AND implies multiply)