Let's address the problem step by step.
### Step 1: Calculate the Expected Number of Tickets per Spin
Given the ticket values and their corresponding probabilities, we find the expected number of tickets by multiplying each ticket value by its probability and then summing these products.
The ticket values are:
- 1 ticket with probability 0.15
- 2 tickets with probability 0.20
- 3 tickets with probability 0.20
- 5 tickets with probability 0.10
- 10 tickets with probability 0.10
- 25 tickets with probability 0.04
- 100 tickets with probability 0.01
Multiplying each ticket value by its probability:
[tex]\[ \text{Expected tickets per spin} = (1 \times 0.15) + (2 \times 0.20) + (3 \times 0.20) + (5 \times 0.10) + (10 \times 0.10) + (25 \times 0.04) + (100 \times 0.01) \][/tex]
Summing these values:
[tex]\[ \text{Expected tickets per spin} = 0.15 + 0.40 + 0.60 + 0.50 + 1.00 + 1.00 + 1.00 = 4.65\][/tex]
So, the average number of tickets expected from one spin is 4.65.
### Step 2: Calculate the Expected Number of Tickets for 20 Spins
Given the expected number of tickets per spin, we now calculate how many tickets can be expected from 20 spins.
[tex]\[ \text{Expected tickets for 20 spins} = \text{Expected tickets per spin} \times 20 \][/tex]
Using the earlier result of 4.65 tickets per spin:
[tex]\[ \text{Expected tickets for 20 spins} = 4.65 \times 20 = 93\][/tex]
So, for 20 spins, you can expect to win 93 tickets.
### Summary
To answer the specific question from the user:
- The average number of tickets per spin is 4.65.
- For 20 spins, the expected number of tickets is 93.
