2. A bowl has 34 red M&Ms and 18 green M&Ms. Joan randomly chooses a M&M, eats it, and
then chooses another M&M. Round to the nearest percent.
(a) What is the probability that both M&Ms are green? Show your work.
(b) What is the probability that Joan will eat a red M&M then a green M&M? Show your
work.

After picking one green M&M, there are 17 green M&Ms left and 51 M&Ms total for the second pick, so the probability of choosing another green M&M is 17/51.

So, the probability of choosing two green M&Ms is:

(18/52) * (17/51) ≈ (0.3462) * (0.3333) ≈ 0.1154

(b) Probability of choosing a red M&M then a green M&M:

For the first pick, the probability of choosing a red M&M is 34/52.

After picking one red M&M, there are 18 green M&Ms left and 51 M&Ms total for the second pick, so the probability of choosing a green M&M is 18/51.

So, the probability of choosing a red M&M then a green M&M is:

(34/52) * (18/51) ≈ (0.6538) * (0.3529) ≈ 0.2308

Round to the nearest percent:

(a) Probability of both M&Ms being green ≈ 12%

(b) Probability of eating a red M&M then a green M&M ≈ 23%

Step-by-step explanation:

Of course! Let's break down each step of solving the problem:

(a) Probability of choosing two green M&Ms:

Step 1: Calculate the total number of M&Ms in the bowl.

Total M&Ms = 34 (red) + 18 (green) = 52 M&Ms

Step 2: Determine the probability of choosing a green M&M on the first pick.

Probability of first pick being green = Number of green M&Ms / Total M&Ms

Probability of first pick being green = 18 / 52

Step 3: Determine the probability of choosing a green M&M on the second pick, given that the first pick was green.

Since one green M&M has already been picked, there are now 17 green M&Ms left out of 51 M&Ms remaining.

Probability of second pick being green = (Number of remaining green M&Ms) / (Total remaining M&Ms)

Probability of second pick being green = 17 / 51

Step 4: Multiply the probabilities from Steps 2 and 3 to find the overall probability of choosing two green M&Ms.

Probability of both M&Ms being green = (Probability of first pick being green) * (Probability of second pick being green)

(b) Probability of choosing a red M&M then a green M&M:

Step 1: Calculate the total number of M&Ms in the bowl. (Same as in part a)

Step 2: Determine the probability of choosing a red M&M on the first pick.

Probability of first pick being red = Number of red M&Ms / Total M&Ms

Probability of first pick being red = 34 / 52

Step 3: Determine the probability of choosing a green M&M on the second pick, given that the first pick was red.

Probability of second pick being green = (Number of green M&Ms) / (Total M&Ms after first pick)

Probability of second pick being green = 18 / 51

Step 4: Multiply the probabilities from Steps 2 and 3 to find the overall probability of choosing a red M&M then a green M&M.

Probability of eating a red M&M then a green M&M = (Probability of first pick being red) * (Probability of second pick being green)

Finally, round the probabilities to the nearest percent for both parts (a) and (b).