Question

A missile guidance system has five fail-safe components. The probability of each failing is 0.05. Find these probabilities

Answer 1

do you mean probability that all 5 will fail? then it will be \[0.05 \times 0.05 \times 0.05 \times 0.05 \times 0.05\]

Answer 2

What are the probabilities required? The question is not complete.

Answer 3

A missile guidance system has five fail-safe components. The probability of each failing is 0.30. Find the probability that exactly four will fail

Answer 4

P(4 fail) = 0.3 * 0.3 * 0.3 * 0.3

Answer 5

your question changed.o.O

Answer 6

5*.3 * .3 * .3 * .3*.7

Answer 7

assuming independence

Answer 8

Because each component is fail-safe, the failure of any one of the 5 components does not affect the others.
The compound event 4 failures is made up of 4 separate and independent sub-events. Therefore the probability of the compound event is the product of the separate probabilities of each sub-event:
P(4 fail) = 0.3 * 0.3 * 0.3 * 0.3

Answer 9

remember there are 5 components...so to get exactly 4 failures you need to have one of the following

(F=fail, N=not Fail)

FFFFN
FFFNF
FFNFF
FNFFF
NFFFF

each has prob \(.3\times.3\times.3\times.3\times.7\)

adding them all up gives \(5\times.3\times.3\times.3\times.3\times.7\)