A bag of 29 tulip bulbs contains 12 red tulip bulbs, 9 yellow tulip bulbs, and 8 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 nothing.

[tex]= P(\text{Red tulip in first draw})\times P(\text{Red tulip in second draw})\\\\= \frac{12}{29}\times \frac{11}{28} = \frac{132}{812} = 0.162561576355 \approx 0.163[/tex]

Probability that two random selected tulip is red is 0.163

b) P(First tulip is red and second is yellow)

[tex]= P(\text{Red tulip in first draw})\times P(\text{Yellow tulip in second draw})\\\\= \frac{12}{29}\times \frac{9}{28} = \frac{108}{812} = 0.133004926108 \approx 0.133[/tex]

Probability that first tulip is red and second is yellow is 0.133

c) P(First tulip is yellow and second is red)

[tex]= P(\text{Yellow tulip in first draw})\times P(\text{Red tulip in second draw})\\\\= \frac{9}{29}\times \frac{12}{28} = \frac{108}{812} = 0.133004926108 \approx 0.133[/tex]

Probability that first tulip is yellow and second is red is 0.133

d) P(one bulb is red and one is yellow)

[tex]= P(\text{Red tulip in first draw})\times P(\text{Yellow tulip in second draw}) + P(\text{Yellow tulip in first draw})\times P(\text{Red tulip in second draw}) \\= 0.133004926108 + 0.133004926108 \\= 0.266009852216 \approx 0.266[/tex]