A bag of 33 tulip bulbs contains 14 red tulip bulbs, 12 yellow tulip bulbs, and

Question

A bag of 33 tulip bulbs contains 14 red tulip bulbs, 12 yellow tulip bulbs, and 7 purple tulip bulbs. (a) What is the probability that 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? (a) The probability that both bulbs are red is (Round to three decimal places as needed.)

Explanation / Answer

note that all the questions involve selecting 2 bulbs.
so the denominator will be 33 for the 1st selection
and 32 for the 2nd selection.
A)
P[both red] = [14/33] * [13/32]

= 91/528 = 0.172

b)
P[1st red, 2nd yellow] = [14/33] * [10/32]

= 35/264 = 0.132

C)
P[1st yellow, 2nd red] = [10/33] * [14/32]

= 35/264 = 0.132

d)
P[one red, one yellow] = P[1st red, 2nd yellow] + P[1st yellow, 2nd red]

= [14/33] * [10/32] + [10/33] * [14/32]

= (35/264) + (35/264)

= 0.265

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