Question

A homeowner plants 6 bulbs selected at random from a box containing 5 tulip bulbs and 4 daffodil bulbs. What is the probability that he planted 2 daffodil bulbs and 4 tulip bulbs?

Answer 1

Answer:

Required probability = 0.3571

Step-by-step explanation:

We are given that a homeowner plants 6 bulbs selected at random from a box containing 5 tulip bulbs and 4 daffodil bulbs.

Number of ways of selecting 2 daffodil bulbs from total of 4 daffodil bulbs is given by = $^{4} C_2$ = $\frac{4!}{2!*2!}$ = 6

Number of ways of selecting 4 tulip bulbs from total of 5 tulip bulbs is given by = $^{5} C_4$ = $\frac{5!}{4!*1!}$ = 5

And Number of ways of selecting 6 bulbs from total of 9 bulbs in the box is given by = $^{9} C_6$ = $\frac{9!}{6!*3!}$ = 84

So, probability that he planted 2 daffodil bulbs and 4 tulip bulbs = $\frac{^{4} C_2*^{5} C_4}{^{9} C_6}$

                                   =  $\frac{6*5}{84}$ = 30/84 = 0.3571

Therefore, required probability = 0.3571.

Answer 2

We are given that a homeowner plants 6 bulbs selected at random from a box containing 5 tulip bulbs and 4 daffodil bulbs.

Number of ways of selecting 2 daffodil bulbs from total of 4 daffodil bulbs is given by =  =  = 6

Number of ways of selecting 4 tulip bulbs from total of 5 tulip bulbs is given by =  =  = 5

And Number of ways of selecting 6 bulbs from total of 9 bulbs in the box is given by =  =  = 84

So, probability that he planted 2 daffodil bulbs and 4 tulip bulbs =

                                  =   = 30/84 = 0.3571

Therefore, required probability = 0.3571.