addison sells 100 tickets for $10 each for a raffle. there is 1 award for $100, 4 awards for $50, and 10…
addison sells 100 tickets for $10 each for a raffle. there is 1 award for $100, 4 awards for $50, and 10 awards for $30. the remaining proceeds go to hosting the contest. which table correctly displays the probability distribution?\n\ndistribution of awards\n| prize | $p(x)$ |\n| none | 0.85 |\n| $30 | 0.01 |\n| $50 | 0.04 |\n| $100 | 0.10 |\n\ndistribution
Answer
Answer:
None of the provided tables are correct. The correct probability - distribution table should be:
| Prize | $P(x)$ |
|---|---|
| none | $0.85$ |
| $$30$ | $0.1$ |
| $$50$ | $0.04$ |
| $$100$ | $0.01$ |
Explanation:
Step1: Calculate number of non - winning tickets
Total tickets = 100. Number of winning tickets: 1 (for $100$) + 4 (for $50$) + 10 (for $30$)=1 + 4+10 = 15. Non - winning tickets = 100 - 15=85. Probability of winning nothing $P(\text{none})=\frac{85}{100}=0.85$.
Step2: Calculate probability of $30$ prize
Number of $30$ prizes is 10. Probability $P(30)=\frac{10}{100}=0.1$.
Step3: Calculate probability of $50$ prize
Number of $50$ prizes is 4. Probability $P(50)=\frac{4}{100}=0.04$.
Step4: Calculate probability of $100$ prize
Number of $100$ prizes is 1. Probability $P(100)=\frac{1}{100}=0.01$.