Historically, 70% of all attendees of a sales conference are men and only 30% wo

Question

Historically, 70% of all attendees of a sales conference are men and only 30% women.

If you pick a random sample of 5 people at the conference, find the probabilities that:

a. All women are selected.

b. Three men are selected.

c. Less than 3 women are selected.

Historically, 70% of all attendees of a sales conference are men and only 30% women.

If you pick a random sample of 5 people at the conference, find the probabilities that:

a. All women are selected.

b. Three men are selected.

c. Less than 3 women are selected.

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a.
P( X = 5 ) = ( 5 5 ) * ( 0.3^5) * ( 1 - 0.3 )^0
= 0.0024

b.
P( X = 3 ) = ( 5 3 ) * ( 0.7^3) * ( 1 - 0.7 )^2
= 0.3087

c.
P( X < 3) = P(X=2) + P(X=1) + P(X=0)
= ( 5 2 ) * 0.3^2 * ( 1- 0.3 ) ^3 + ( 5 1 ) * 0.3^1 * ( 1- 0.3 ) ^4 + ( 5 0 ) * 0.3^0 * ( 1- 0.3 ) ^5
= 0.8369

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