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Question
A lottery with 600 tickets gives one prize of ₹ 200, four prizes of ₹ 100, and six prizes of ₹ 50. If the ticket costs is ₹ 2, find the expected winning amount of a ticket
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Solution
Given, total number of tickets = 600
Prizes to be given: One prize of Rs. 200
Four prizes of ₹ 100
Six prizes of ₹ 50
Let ‘X’ be the random variable denotes the winning amount and it can take the values 200, 100 and 50.
Probability of winning ₹ 200 = `1/600`
Probability of winning ₹ 100 = `4/600`
Probability of winning ₹ 50 = `6/600`
∴ Probability mass function is
| x | 200 | 100 | 50 |
| F(x) | `1/600` | `4/600` | `6/600` |
∴ E(X) = 200 `sum x f(x)`
= `200/600 + 400/600 + 300/600`
= `900/600`
= 1.5
Expected winning amount = Amount won – Cost of lottery
= 1.50 – 2.00
= – 0.50
i.e., Loss of ₹ 0.50
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