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In a raffle draw, 1000 raffle tickets are sold for ₹ 1 each. Each has an equal chance of winning…
In a raffle draw, 1000 raffle tickets are sold for ₹ 1 each. Each has an equal chance of winning. First prize is ₹ 300, second prize is ₹ 200, and third prize is ₹ 100. Let X denote the net gain from the purchase of one ticket.
(a)[2.0]
Construct the probability distribution of X.
(b)[2.0]
Find the probability of winning any money in the purchase of one ticket.
(c)[2.0]
Find the expected value of X and interpret its meaning.
Answer
Answer (a)
Official answer key| X | 299 | 199 | 99 | -1 |
| P(X) | .001 | .001 | .001 | .997 |
Final answer: X = 299, 199, 99, -1 with P(X) = 0.001, 0.001, 0.001, 0.997
Answer (b)
Official answer keyLet W denote the event of winning any money in the purchase of one ticket. Using the table: $P(W) = P(299) + P(199) + P(99) = 0.001 + 0.001 + 0.001 = 0.003$
Final answer: 0.003
Answer (c)
Official answer key$E(X) = (299)(0.001) + (199)(0.001) + (99)(0.001) + (-1)(0.997) = -0.4$
Negative expectation means that a person will lose money even if multiple tickets are purchased.
Final answer: -0.4
From ISC 2025 Practice Mathematics, question 126.
Check your working with the Probability distribution calculator: find k, the mean, variance and standard deviation of a random variable, with the working table.