14 Yingtai visits her local gym regularly.
After each visit she chooses one item to eat from the gym's cafe.
This could be an apple, a banana or a piece of cake.
She chooses the item independently each time.
The probability that Yingtai chooses each of these items on any visit is given by:
$$\begin{aligned}
\mathrm { P } ( \text { Apple } ) & = 0.2
\mathrm { P } ( \text { Banana } ) & = 0.35
\mathrm { P } ( \text { Cake } ) & = 0.45
\end{aligned}$$
For any four randomly selected visits to the gym, find the probability that Yingtai chose:
14
- at least one banana.
[0pt]
[2 marks]
14 - the same item each time.
| 14 | apple twice and cake twice |