(i)[1]
Show that $p$ equals $0.3$.
(ii)[4]
Given that Maria switches on the radio and hears a male presenter, find the probability that the radio had been set to station $2$.
Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
Maria has $3$ stations already stored on her radio. When she turns the radio on, there is a probability of $0.3$ that it will tune to station $1$, a probability of $0.45$ that it will tune to station $2$, and a probability of $0.25$ that it will tune to station $3$. On station $1$, the probability that the presenter is male is $0.1$; on station $2$, the probability that the presenter is male is $0.85$; and on station $3$, the probability that the presenter is male is $p$. When Maria switches on the radio, the probability that it is on station $3$ with a male presenter is $0.075$.