Chapter 11.9, Problem 5E

To determine

To calculate:the probability that I win the grand prize and my friend wins the runner up prize.

Answer to Problem 5E

1. The winning the grand prize and runner up prize by friend are independent events.
2. The probability of win the grand prize is $\frac{1}{30}$ .
3. The probability of win the runner up prize by friend is $\frac{1}{29}$ .
4. The probability that I win the grand prize and my friend win the runner up prize is $\frac{1}{15}$ .

Explanation of Solution

Given information :

total ticket sold = $30$

Calculation :

1. The probability of winning the grand prize by me and my friend win the runner up prize, are independent because probability of winning grand prize by me doesn’t affect the probability to winning runner up prize by him.
2. To find the probability that I win the grand prize, first find the total no of possibilities of winning prize,
total number of possibilities = $30$

then divide the number of grand prize by number of total possibilities,

probability = $\frac{1}{30}$

3. To find the probability that my friend win the runner up prize, first find the total possibilities which are 29 because already one ticket was sold,
Total possibilities = $29$

Probability = $\frac{1}{29}$

4. To find the probability that me win the grand prize and my friend runner up so, we have to choose two out of thirty,
Total possibilities = $30$

Probability = $\frac{2}{30}$

= $\frac{1}{15}$

Hence,

1. The winning the grand prize and runner up prize by friend are independent events.
2. The probability of win the grand prize is $\frac{1}{30}$ .
3. The probability of win the runner up prize by friend is $\frac{1}{29}$ .
4. The probability that I win the grand prize and my friend win the runner up prize is . $\frac{1}{15}$