Question

A bag of 27 tulip bulbs contains 11 red tulip bulbs, 8 yellow tulip bulbs, and 8 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag.

(a) What is the probability that the two randomly selected tulip bulbs are both red?
(b) What is the probability that the first bulb selected is red and the second yellow?
(c) What is the probability that the first bulb selected is yellow and the second red?
(d) What is the probability that one bulb is red and the other yellow?

Answer 1

To find the probability of independent events, we can use the formula: P(A and B) = P(A) x P(B). Let's calculate the probabilities for each part of the question. (a) P(both red) = 5/39, (b) P(first red, second yellow) = 22/175, (c) P(first yellow, second red) = 22/175, (d) P(one red, one yellow) = 176/351.

Step-by-step explanation:

To find the probability of independent events, we can use the formula:

P(A and B) = P(A) x P(B)

Let's calculate the probabilities for each part of the question:

(a) P(both red) = P(red1) x P(red2) = (11/27) x (10/26) = 110/702 = 5/39

(b) P(first red, second yellow) = P(red1) x P(yellow2) = (11/27) x (8/26) = 88/702 = 22/175

(c) P(first yellow, second red) = P(yellow1) x P(red2) = (8/27) x (11/26) = 88/702 = 22/175

(d) P(one red, one yellow) = [P(red1) x P(yellow2)] + [P(yellow1) x P(red2)] = [(11/27) x (8/26)] + [(8/27) x (11/26)] = 176/702 + 176/702 = 352/702 = 176/351