Question

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.

Answer 1

a) 0.163 b) 0.133 c) 0.133 d) 0.266

Explanation:

We are given the following information:

Total number of tulips in bag = 29

Number of red tulips = 12

Number of yellow tulips = 9

Number of purple tulips = 8

Formula:

`\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}`

a) P(Both tulips are red)

`= P(\text{Red tulip in first draw})* P(\text{Red tulip in second draw})\\\\= (12)/(29)* (11)/(28) = (132)/(812) = 0.162561576355 \approx 0.163`

Probability that two random selected tulip is red is 0.163

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

`= P(\text{Red tulip in first draw})* P(\text{Yellow tulip in second draw})\\\\= (12)/(29)* (9)/(28) = (108)/(812) = 0.133004926108 \approx 0.133`

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

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

`= P(\text{Yellow tulip in first draw})* P(\text{Red tulip in second draw})\\\\= (9)/(29)* (12)/(28) = (108)/(812) = 0.133004926108 \approx 0.133`

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

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

`= P(\text{Red tulip in first draw})* P(\text{Yellow tulip in second draw}) + P(\text{Yellow tulip in first draw})* P(\text{Red tulip in second draw}) \\= 0.133004926108 + 0.133004926108 \\= 0.266009852216 \approx 0.266`