Respuesta :
Answer:
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
