Question

A bag of 29 tulip bulbs contains 10 red tulip​ bulbs, 10 yellow tulip​ bulbs, and 9 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

a.The probability that two randomly selected tulip bulbs both are red=
`(45)/(406)`.

b.The probability that the first bulb selected is red and second yellow=
`(50)/(406)`.

c.The probability that the first bulb selected is yellow and the second red=
`(50)/(406)`.

d.The probability that one bulb is red and other yellow=
`(50)/(203)`.

Explanation:

Given

Total number of bulbs= 29

Number of bulbs of red=10

Number of yellow bulbs=10

Number of purple bulbs=9

Formula of probability, P(E)=
`(favourable \; cases)/(total\;number\; of \; cases)`

a.The probability that two randomly selected tulip bulbs are both red=
`(10)/(29)*(9)/(28)=(45)/(406)`.

b.The probability of getting first bulb is red=
`(10)/(29)`.

The probability of getting second bulb is yellow=
`(10)/(28)`

Hence,the probability that the firs bulb selected is red and the second bulb yellow=
`(10)/(29)*(9)/(28)=(45)/(406)`

c. The probability of getting firs bulb is yellow =
`(10)/(29)`

The probability of getting second bulb is red=
`(10)/(28)`

Hence,the probability that the firs bulb selected is yellow and the second bulb red=
`(10)/(29)*(10)/(28)=(50)/(406)`.

d.The probability of getting first bulb is red and second is yellow=
`(50)/(406)`

The probability of getting first bulb is yellow and second is red=
`(50)/(406)`

The probability that one bulbe is red and other is yellow= probability of getting first bulb is red and other yellow+ probability of getting first bulb is yellow and other is red

Hence, the probability of getting one bulb is red and other is yellow=
`(50)/(406)+(50)/(406)=(50)/(203)`