Question #5ac9e

2 Answers

#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#.

Dec 6, 2017

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)