Question

A bag of 30 tulip bulbs contains 13 red tulip​ bulbs, 10 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?

Answer 1

solution:

From the given information

No.of red tulip bulbs = 13

No.of yellow tulip bulbs = 10

No.of purple tulip bulbs = 7

Total no.of bulbs = 30

When two bulbs are randomly selected without replacement

n(S) = 30*29 = 870

a)

Let A = event that randomly selected two bulbs are red

n(A) = 13*12 = 156

Probability that the two randomly selected bulbs are both are red = P(A)

= n(A) / n(S)

= 156 / 870

= 0.1793

  Probability that the two randomly selected bulbs are both are red = 0.1793

b)

Let B = event that first bulb is red and second bulb is yellow

n(B) = 13*10 = 130

Probability that the first bulb is red and second bulb is yellow = P(B)

= n(B) / n(S)

= 130 / 870

= 0.1494

Probability that the first bulb is red and second bulb is yellow = 0.1494

c)

Let C = event that first bulb is yellow and second bulb is red

n(C) = 10*13 = 130

Probability that the first bulb is yellow and second bulb is red = P(C)

= n(C) / n(S)

= 130 / 870

= 0.1494

Probability that the first bulb is yellow and second bulb is red = 0.1494

d)

Probability that one bulb is red and other is yellow = P(RY) + P(YR)

= P(B) + P(C)

= 130 / 870 + 130 / 870

= 260 / 870

=~ 0.2989

Probability that one bulb is red and other is yellow = 0.2989