Answer:
0.55
Missing Statement:
At a carnival, one game costs $1 to play. The contestant gets one shot in an attempt to bust a balloon. Each balloon
contains a slip of paper with one of the following messages:
- Sorry, you do not win, but you get your dollar back. (The contestant has not lost the $1 cost.)
- Congratulations, you win $2. (The contestant has won $1.)
- Congratulations, you win $5. (The contestant has won $4.)
- Congratulations, you win $10. (The contestant has won $9.)
If the contestant does not bust a balloon, then the $1 cost is forfeited. The table below displays the probability
distribution of the discrete random variable, or net winnings for this game
Net Winnings −1 0 1 4 9
<u><em>Probability</em></u> 0.25 ? 0.3 0.08 0.02
Step-by-step explanation:
First we find of the missing probability for net winnings of 0, in which case:
When you receive the message, “Sorry, you do not win, but you get your dollar back,” then your net winnings is 0$.
The probability of winning 0$ is = 1 - 0.25 - 0.3 - 0.08 -0.02 = 0.35
So now we have the complete details:
Net Winnings −1 0 1 4 9
Probability 0.25 0.35 0.3 0.08 0.02
Now we need to find ,the net amount that a contestant should expect to win is the expected value of the probability distribution.
Expected value of probability distribution = −1(0.25 ) +0 (0.35 ) + 1(0.3 ) +4 (0.08 ) + 9(0.02 )
Expected value of probability distribution = 0.55
<u><em>The net amount that a contestant should expect to win per game if the game were to be played many times is 0.55</em></u>
