Find the probability that Lucca eats at least one banana in a particular day.

Find the expected number of weeks in the year in which Lucca eats no bananas.

let $X$ be the number of bananas eaten in one day

$X \sim {\text{Po}}(0.2)$

${\text{P}}(X \geqslant 1) = 1 - {\text{P}}(X = 0)$     (M1)

$= 0.181{\text{ }}( = 1 - {{\text{e}}^{ - 0.2}})$     A1

[2 marks]

EITHER

let $Y$ be the number of bananas eaten in one week

${\text{Y}} \sim {\text{Po}}(1.4)$     (A1)

${\text{P}}(Y = 0) = 0.246596 \ldots {\text{ }}( = {{\text{e}}^{ - 1.4}})$     (A1)

OR

let $Z$ be the number of days in one week at least one banana is eaten

$Z \sim {\text{B}}(7,{\text{ }}0.181 \ldots )$     (A1)

${\text{P}}(Z = 0) = 0.246596 \ldots$     (A1)

THEN

$52 \times 0.246596 \ldots$     (M1)

$= 12.8{\text{ }}( = 52{{\text{e}}^{ - 1.4}})$     A1

[4 marks]