Enter the probability as a fraction. P(at least one green) =

Question

Suppose that you have 9 cards. 4 are green and 5 are yellow. The 4 green cards are numbered 1, 2, 3, and 4. The 5 yellow cards are numbered 1, 2, 3, 4, and 5. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, and with replacement.

• G₁ = first card is green

• G₂ = second card is green

Answer 1

Based on your comments below, the problems is this:

Suppose that you have 8 cards. 3 are green and 5 are yellow. The 3 green cards are numbered 1, 2, and 3. The 5 yellow cards are numbered 1, 2, 3, 4, and 5. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, and without replacement. • G1 = first card is green • G2 = second card is green Part (a) Draw a tree diagram of the situation. (Enter your answers as fractions.) WebAssign Plot Enter the probability as a fraction. P(at least one green) =

You can make a tree like this to help determine the answer:

The probability that at least 1 card is green comes in three ways. The probability that you get green for the 1st card and green on the second is 9/64 (you get that by multiplying 3/8 and 3/8). The probability that you get green for the 1st card and yellow on the second is 15/64 (3/8 times 5/8). The probability that you get yellow for the 1st card and green on the second is 15/64 (5/8 times 3/8). That means the probability of getting at least one green card is 9/64 + 15/64 + 15/64 = 39/64