Question

shelley buys a lottery ticket. the ticket has several ways to win.
the table below shows the different ways to win, the probability of winning each way, and how much money each win results in. every time shelley buys a ticket, she can win money each way.
given the probabilities and payout values in this table, what is the expected value of shelleys ticket?

Explanation:

Step1: Convert percentages to decimals

$42\% = 0.42$, $38\%=0.38$, $19\% = 0.19$, $1\%=0.01$

Step2: Calculate the product of probability and winnings for each way

• For Way 1: $0.42\times1 = 0.42$
• For Way 2: $0.38\times5=1.9$
• For Way 3: $0.19\times10 = 1.9$
• For Way 4: $0.01\times100=1$

Step3: Sum up the products

$0.42 + 1.9+1.9 + 1$
$=0.42+(1.9\times2)+1$
$=0.42 + 3.8+1$
$=5.22$

Answer:

$5.22$