6. aA box in a certain supply room contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs. Suppose that three bulbs are randomly selected. a. What is the probability that exactly one of the selected bulbs are rated 75-watt? b. What is the probability that all three of the elected bulbs have the same rating? c. What is the probability that one bulb of each type is selected? d. What is the probability that at least two of the selected bulbs are rated 75-watt?

A) 0.2967

B) 0.0747

C) 0.2637

D)0.6933

Step-by-step explanation:

We are told the box contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs.

Thus, total number of bulbs = 4 + 5 + 6 = 15 bulbs

This is a combination problem.

Thus;

A) probability that exactly one of the selected bulbs are rated 75-watt will be = ((6C2) × (9C1))/(15C3)

= (15 × 9)/455

= 0.2967

B) probability that all three of the elected bulbs have the same rating;

Number of ways to select three 40 watt bulbs out of the 4 in the box = 4C1 = 4!/(3! × 1!) = 4

Number of ways to select three 60 watt bulbs out of the 5 in the box = 5C1 =

5!/(3! × 2!) = 10

Number of ways to select 75 watt bulbs out of the 6 in the box = 6C1 = 6!/(3! × 3!) = 20

Total number of ways = 4 + 10 + 20 = 34.

Thus, probability that all three of the elected bulbs have the same rating = 34/15C3 = 34/455

= 0.0747

C) probability that one bulb of each type is selected =

[(4C1) × (5C1) × (6C1)]/(15C3)

= (4 × 5 × 6)/455

= 0.2637

D) probability that at least two of the selected bulbs are rated 75-watt =

[(4C1 × 5C1 × 6C2)/15C3] + 6C3/15C3

= (4 × 5 × 15/455) + 20/455

= 0.6493 + 0.044

= 0.6933

is means division by fractions

step-by-step explanation: