Answer :
Answer:
Probability that exactly three of the selected bulbs are rated 75-W is 0.044.
Step-by-step explanation:
We are given that a box in a certain supply room contains four 40-W light bulbs, five 60-W bulbs, and six 75-W bulbs.
And we have to find the probability that exactly three of the selected bulbs are rated 75-W.
Here, we will use Combinations for selection procedure, i.e.;
[tex]^{n} C_r = \frac{n!}{r! \times (n-r) !}[/tex]
So, number of ways of selecting three 75-W rated bulbs from total of six 75-W rated bulbs in a box is given by = [tex]^{6} C_3[/tex]
Total number of ways of selecting three bulbs from total of 15 bulbs (4 + 5 + 6) in a box = [tex]^{15} C_3[/tex]
Therefore, probability that exactly three of the selected bulbs are rated 75-W is given as = [tex]\frac{^{6} C_3}{^{15} C_3}[/tex] = [tex]\frac{\frac{6!}{3! \times 3!} }{\frac{15!}{3! \times 12!} }[/tex]
= [tex]\frac{6!}{3!} \times \frac{12!}{15!}[/tex] = [tex]120 \times \frac{1}{2730}[/tex] = [tex]\frac{4}{91}[/tex]
= 0.044
Hence, the required probability is 0.044.