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]