Three missiles are fired at an enemy arsenal. The probabilities the individual missile will hit the arsenal are 0.75, 0.85, and

Question

Nataly_w [17]

4 years ago

14

Three missiles are fired at an enemy arsenal. The probabilities the individual missile will hit the arsenal are 0.75, 0.85, and

0.9. Find the probability that at least two of the missiles hit the arsenal..

Mathematics

1 answer:

Fantom [35] · Answer 1 · 2022-01-30T23:31:48+03:00

The probability that at least two of the missiles hit the arsenal:
P ( x ≥ 2 ) = P ( x = 2 ) + P ( x = 3 )
P ( x = 2 ) = 0.75 · 0.85 · 0.1 + 0.85 · 0.9 · 0.25 + 0.75 · 0.9 · 0.15 =
= 0.06375 + 0.10125 + 0.19125 = 0.35625
P ( x = 3 ) = 0.75 · 0.85 · 0.9 = 0.57375
P ( x ≥ 2 ) = 0.35625 + 0.57375 = 0.93
Answer:
The probability is 0.93 or 93%.