Question

In a school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random.
Find the probability that
a) exactly 5 have access to the internet.
b) at least 6 students have access to the internet.

Answer 1

Answer:

(a.)Computing the probability exactly 5 have access to the internet:

P(X)=5

=8C5p5p(8−5)

=8C5×0.605×0.40(8−5)

=8C5×0.00498=0.27888P(X=5)

=8C5p5(1−p(8−5)

=8C5×0.605×0.40(8−5)

=8C5×0.00498

=0.27888

Therefore, the probability that exactly 5 have access to the internet would be 0.27888.

(b.)Computing the probability that at least 6 have access to the internet: _

P(X≥6)

=P(X=6)+P(X)

=P(X=8)

=8C6×0.606×0.40(8−6)+8C7×0.607×0.4(8−7)+8C8×0.608×0.40(8−8)

=8C6×0.00747+8C7×0.01120+8C8×0.01680

=0.31556