A certain newspaper reports that about 20% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.(a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.)P(0) =P(1) =P(2) =P(3) =P(4) =

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Asked Oct 19, 2019
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A certain newspaper reports that about 20% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.

(a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.)
P(0) =
P(1) =
P(2) =
P(3) =
P(4) =

 

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Expert Answer

Step 1

From the provided information, the probability that all prison parolees become repeat offenders is 0.20. So, the probability that all prison parolees do not become repeat offenders will be (1-0.20) 0.80, which is assumed as probability of success (p). Consider X be random variable which represents the number of parolees who does not become a repeat offender. The number of trials (n) is 4. The binomial distribution will be used for calculating the probability as:

P(X=r) C,(p) (1-p)
n-7
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P(X=r) C,(p) (1-p) n-7

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Step 2

Now, the required probabilities for r=0...

P(0)C,(0.8)'(1-0.80)
-1x (1)x (0.0016)
= 0.0016
P(1)C(0.8)(1-0.80)
=4x(0.8)x (0.008)
=0.0256
P(2)=C,(0.8) (1-0.80)
6x (0.64) x(0.04)
=0.1536
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P(0)C,(0.8)'(1-0.80) -1x (1)x (0.0016) = 0.0016 P(1)C(0.8)(1-0.80) =4x(0.8)x (0.008) =0.0256 P(2)=C,(0.8) (1-0.80) 6x (0.64) x(0.04) =0.1536

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