Question

Out of 1,000 tickets in a raffle, one ticket will win a $950 prize. The remaining tickets will win nothing. X is the payoff for one ticket in the raffle. Write the probability distribution of X in the table below. Write each probability as an exact decimal.

Answer 1

The probability distribution of X for this raffle is as follows:

X P(X)

$950 1/1000

$0 999/1000

To calculate the probability of winning the prize, we divide the number of winning tickets by the total number of tickets. In this case, there is only 1 winning ticket out of a total of 1000 tickets, so the probability of winning the prize is 1/1000, which we express as an exact decimal as 0.001.

The probability of not winning the prize is equal to the total number of non-winning tickets divided by the total number of tickets. In this case, there are 999 non-winning tickets out of a total of 1000 tickets, so the probability of not winning the prize is 999/1000, which we express as an exact decimal as 0.999.

Together, these probabilities add up to 1, which is the total probability for all possible outcomes.