A cup contains 20 oranges numbered 1, 2, 3, …, 20. The cup is tumbled and then t

Question

A cup contains 20 oranges numbered 1, 2, 3, …, 20. The cup is tumbled and then three organges are chosen at random (without replacement).

(a) What is the probability that the numbers drawn are {18,14,2} in this order?

(b) What is the probability that the numbers drawn are {18,14,2} in any order?

(c) What is the probability that:

(i) the first number drawn is less than 15?

(ii) the first two numbers are both less than 15?

(iii) all three numbers are less than 15?

(d) A lottery ticket costs $1 and pays off $50,000 if the numbers {18,14,2} are chosen in that order. What is the expected payoff from entering the lottery (expected gain – expected cost)?

Explanation / Answer

a) Probability = 1/[20*19*18]=1/6840

b) Probability = 3C3/[20C3]= 6/6840

c) 1 Probbility = 14/20

2 Probability = 14 * 13/[20*19]=91/190

3) Probablity = 14*13*12/[20*19*18]=0.3192

Expected payoff = 50000/6840-1=6.31 dollars

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