A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner

Question

A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w = amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers.)

Value of w (in dollars) Probability 1 10 0.2 25 A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers value of w (in dollars) Probability 1 16 x 10 25

Explanation / Answer

Total number of cases possible = 5C2 = 10

There would be only 1 case in which he will win $1 i.e. when both the slips selected has $1.

So,

P(Winning $1) = 1/10 = 0.1

Given,

P(Winning $10) = 2/10 = 0.2

So,

P(Winning $25) = 1 - (0.1 + 0.2) = 0.7

[We can check it also. Total number of possibilities of winning $25 is 7. So. P(Winning $25) = 7/10 = 0.7]

Hence,

The probability distribution will be:

w P(w) 1 0.1 10 0.2 25 0.7

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