Question

a bag of 29 tulip bulbs contains 11 red tulip bulbs, 11 yellow tulip bulbs, and 7 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? (a) the probability that both bulbs are red is 0.135. (round to three decimal places as needed.) (b) the probability that the first bulb is red and the second is yellow is 0.149. (round to three decimal places as needed.) (c) the probability that the first bulb is yellow and the second is red is . (round to three decimal places as needed.)

Explanation:

Step1: Calculate probability of first - yellow and second - red

The probability that the first bulb is yellow is $\frac{11}{29}$ since there are 11 yellow bulbs out of 29 total bulbs. After selecting a yellow bulb first, there are 28 bulbs left. The probability that the second bulb is red given that the first is yellow is $\frac{11}{28}$ since there are 11 red bulbs remaining.
The probability of the two - step event is the product of the probabilities of each step.
$P=\frac{11}{29}\times\frac{11}{28}$

Step2: Compute the value

$P=\frac{121}{812}\approx0.149$

Answer:

0.149