HSC Science (Computer Science) 11thMaharashtra State Board
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# Suppose that 80% of All Families Own a Television Set. If 5 Families Are Interviewed At Random, Find the Probability that - HSC Science (Computer Science) 11th - Mathematics and Statistics

ConceptConditional Probability

#### Question

Suppose that 80% of all families own a television set. If 5 families are interviewed at  random, find the probability that
a. three families own a television set.
b. at least two families own a television set.

#### Solution

X = Number of families who own a television set.
P = Probability of families who own a television set.

P=80%=80/100=4/5

q=1-p=1-4/5=1/5

Given n=5, X~B(5,4/5)

The p.m.f. or X is given as

P(X=x)=""^nC_xp^xq^(n-x)

=""^nC_xp^xq^(5-x)

a. P(families own television set)

=P(X=3)

=""^5C_3(4/5)^3(1/5)^(5-3)

=128/625

=0.2048

b. P(At least two families own television set)

P(X>=2)=1-P(X<2)

=1-[P(X=0)+P(X=1)]

=1-[""^5C_0(4/5)^0(1/5)^5+""^5C_1(4/5)^1xx(1/5)^4]

=1-(1/55+20/55)

=1-21/3125=3104/3125

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Solution Suppose that 80% of All Families Own a Television Set. If 5 Families Are Interviewed At Random, Find the Probability that Concept: Conditional Probability.
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