Question

A bag of 29 tulip bulbs contains 10 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?

Answer 1

given,

A bag consist of 29 tulip bulbs

a) P(both bulb are red ) =

=
`P(first\ red\ bulb) * P(second\ red\ bulb)`

=
`(10)/(29) * (9)/(28))`

= 0.111

P(both bulb are red ) = 0.111

b) P(first bulb is red and second yellow ) =

=
`P(first\ red\ bulb) * P(second\ yellow\ bulb)`

=
`(10)/(29) * (12)/(28))`

= 0.148

P(first bulb is red and second yellow ) = 0.148

c) P(first bulb is yellow and second red ) =

=
`P(first\ yellow\ bulb) * P(second\ red\ bulb)`

=
`(12)/(29) * (10)/(28))`

=0.148

P(first bulb is yellow and second red ) = 0.148

d) P(one bulb is red and the other​ yellow) =

= P(first bulb is yellow and second red ) + P(first bulb is red and second yellow )

= 0.148 + 0.148

= 0.296

P(one bulb is red and the other​ yellow) = 0.296