Solve the following probability problems. b. Two people are selected to serve as

Question

Solve the following probability problems.

b. Two people are selected to serve as executives from a committee of 3 men and 3 women. In a random selection for the two executives, what is the probability that the selection results in 2 men?

a. 0.40

b. 0.10

c. 0.50

d. 0.22

e. 0.17

f. 0.25

g. 0.20

h. 0.33

c. From 3 men and 2 women, 2 people are selected at random. What is the probability that both people selected are women?

a. 0.25

b. 0.10

c. 0.14

d. 0.05

e. 0.40

f. 0.33

g. 0.20

d. From 3 men and 2 women, 2 people are selected at random. What is the probability that both people selected are men?

a. 0.05

b. 0.14

c. 0.20

d. 0.40

e. 0.25

f. 0.30

g. 0.33

h. 0.10

Explanation / Answer

Solution :

Binomial probability distribution

Formula:

P(k out of n )= n!*pk * qn-k / k! *(n - k)!

( b )

n = 2

p = 3 /6 = 0.5

q = 0.5

P( x = 2 ) = 2!*0.52 * 0.52-2 / 2! *(2 - 2)!

= 0.2500

( c )

n = 2

p = 2 /5 = 0.4

q = 0.6

P( x = 2 ) = 2!*0.42 * 0.62-2 / 2! *(2 - 2)!

= 0.1600

( d )

n = 2

p = 3 /5 = 0.6

q = 0.4

P( x = 2 ) = 2!*0.62 * 0.42-2 / 2! *(2 - 2)!

= 0.3600

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