The process that you monitor relies on 10 cooling pumps. As long as 6 are running the process can continue. In one hour any of the pumps has a 10% chance of being clogged. What is the probability that you will have exactly 4 failures in one hour? Round off to the fourth decimal place.

The probability that you will have exactly 4 failures in one hour = 0.0112

Step-by-step explanation:

Number of pumps = 10

Probability of failure for the pumps in an hour = 0.10

Probability required is the probability that 4 out of 10 pumps fail in an hour.

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = total number of pumps

x = Number of successes required = in this case, number of failure required = 4

p = probability of success = probability that a pump actually fails = 0.1

q = probability of failure = probability that a pump doesn't fail = 0.9

The wordings of the question seem to counter the definition of parameters in the formula, but it is the understanding that is key.

P(X=4) = ¹⁰C₄ (0.1)⁴ (0.9)¹⁰⁻⁴ = 0.011160261 = 0.0112

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47