Sam and Allen have applied for scholarships. The probability that Sam gets a sch

tapetivk

tapetivk

Answered question

2021-11-20

Sam and Allen have applied for scholarships. The probability that Sam gets a scholarship is 0.93. The probability that Allen gets a scholarship is 0.77. The probability they both get scholarships is 0.74.
(a) What is the probability that Sam gets a scholarship but Allen doesnt?

Answer & Explanation

Ceitheart

Ceitheart

Beginner2021-11-21Added 14 answers

Given data:
The probability that Sam got a scholarship is P(s)=0.93.
The probability that Allen got a scholarship is P(a)=0.77.
The probability that both got a scholarship is P(sa)=0.74,
(a)
Write the expression for the probability that Sam got a scholarship but Allen doesnt.
Todd Williams

Todd Williams

Beginner2021-11-22Added 18 answers

(b)
Write the expression for the probability that none of them got a scholarship.
p(B)=1[P(s)+P(a)P(sn)]
Substitute the given values in the above expression.
p(B)=1[0.93+0.770.74]
=0.04
Thus, the probability that that none of them got a scholarship is 0.04.
user_27qwe

user_27qwe

Skilled2021-11-25Added 375 answers

(c)
Write the expression for the conditional probability that Allen also got a scholarship given that Sam got a
scholarship.
p(sa)=P(sa)P(a)
Substitute the given values in the above expression,
p(sa)=0.740.93
=0.7957
Thus, the conditional probability that Allen also got a scholarship given that Sam got a scholarship is 0.7957.
(d)
Write the expression for the conditional probability that Sam will not get a scholarship given that Allen got a
scholarship.
p(sa)=P(sa)P(a)
Substitute the given values in the above expression.
p(sa)=0.770.740.77
=0.03896
Thus, the conditional probability that Sam will not get a scholarship given that Allen got a scholarship is
0.03896.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-11Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-11Added 2605 answers

Answer is given below (on video)

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