(i)[2]
Demonstrate that the probability that Amy loses her original $1$ is $0.64$.
(ii)[4]
Fill in the probability distribution table for Amy’s gain.
(iii)[1]
Find Amy’s expected gain.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
At a funfair, Amy pays $1$ for two tries at making a bell ring by firing a water pistol at it.
• If the bell rings on her first try, she is paid $3$ and stops playing. So, in total, her gain is $2$.
• If the bell rings on her second try, she is paid $1.50$ and stops playing. So, in total, her gain is $0.50$.
• If the bell does not ring in either of the two tries, she loses her original $1$.
The chance that Amy makes the bell ring on any try is $0.2$, independently of the other tries.