a) The probability distribution for a player's winnings is shown in table.
b) The expected winnings for a player are $3.70.
What is probability distribution?
A probability distribution is a mathematical function that describes the likelihood of various variable values. Probability distributions are frequently represented using graphs or probability tables.
a) Since there are 10 possible digits for each of the four positions, there are a total of 10^4 = 10,000 possible sequences of numbers that could be drawn.
Only one of these sequences will be the winning sequence, corresponding to a probability of 1/10,000. If a player wins, the prize is $3,700. Therefore, the probability distribution for a player's winnings is shown in below table.
b) To find the expected winnings, we multiply each possible winning amount by its probability and add the products together:
E(Winnings) = (0) * (9999/10000) + (3700) * (1/10000)
= 37/10
= $3.70 (rounded to two decimal places)
Therefore, the expected winnings for a player are $3.70.
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