Question

Reese, greg, and brad meet once a week for coffee. they each have their favorite caf� and, to be fair, they use randomization to choose where they will meet. each person has a colored marble: red (r) for reese, green (g) for greg, and blue (b) for brad. each week, all three marbles are mixed well in a bag and a marble is selected. the favorite caf� of the person associated with the selected marble is chosen for that week�s meeting. what is the probability that greg will not get to pick the caf� for either of the first two weeks? 0 two-thirds startfraction 4 over 9 endfraction one-half

Answer 1

The probability that Greg will not get to pick the café for either of the first two weeks is 4/9.

Step-by-step explanation:

The student's question involves finding the probability that Greg will not get to pick the café for the first two weeks when meeting with Reese and Brad. Since there are three marbles, one for each person, the probability that Greg's marble (green) is not picked in any given week is 2/3, as there are two marbles that are not green out of three total marbles.

To find the probability that Greg will not get to pick the café for both weeks, we multiply the individual probabilities for each of the two weeks since the events are independent:

Probability for first week = 2/3
Probability for second week = 2/3

Combined probability for two weeks = (2/3) * (2/3) = 4/9

Therefore, the probability that Greg does not get to pick the café for the first two weeks is 4/9.

Answer 2

The probability that Greg will not get to pick the cafe for either of the first two weeks' meetings is 4/9.

How to solve

The probability of Greg not getting to pick the cafe for the first week is 2/3 as there are two marbles out of three that are not green (Greg's color).

For the second week, if Greg hasn't picked the cafe in the first week, the probability that he won't pick it in the second week remains 2/3 because the marble is randomly drawn each week, and the previous week's selection doesn't impact the subsequent week's selection.

Therefore, the probability that Greg will not get to pick the cafe for either of the first two weeks' meetings is the probability that he doesn't pick the cafe for the first week and also doesn't pick it for the second week, which is

2/3 x 2/3 = 4/9

Hence, the probability is 4/9

The Complete Question

Reese, Greg, and Brad meet weekly for coffee, selecting their meeting place randomly using colored marbles: red (R) for Reese, green (G) for Greg, and blue (B) for Brad. Each week, they mix all three marbles in a bag and draw one to determine where they'll meet based on the person associated with the selected marble. What is the probability that Greg will not get to pick the cafe for either of the first two weeks' meetings?

Solution: