6 At a funfair, Amy pays \(
) 1$ for two attempts to make a bell ring by shooting at it with a water pistol.
- If she makes the bell ring on her first attempt, she receives \(
) 3\( and stops playing. This means that overall she has gained \)\\( 2\). - If she makes the bell ring on her second attempt, she receives \(
) 1.50\( and stops playing. This means that overall she has gained \)\\( 0.50\). - If she does not make the bell ring in the two attempts, she has lost her original \(
) 1$.
The probability that Amy makes the bell ring on any attempt is 0.2 , independently of other attempts.
- Show that the probability that Amy loses her original \(
) 1$ is 0.64 . - Complete the probability distribution table for the amount that Amy gains.
| Amy's gain (\$) | | | |
| Probability | 0.64 | | |
- Calculate Amy's expected gain.