A simple lotto ticket has the numbers 1 through 10 printed on it and requires th

Question

A simple lotto ticket has the numbers 1 through 10 printed on it and requires that the ticket purchaser select any 3 of the 10 numbers. If those 3 numbers are drawn-without replacement-from a hat containing the 10 numbers, the ticket holder wins 1^st prize. What is the probability of winning 1^st prize If the ticket holder has 2 of the 3 numbers drawn, they win 2^nd prize. What is the probability of winning 2^nd prize For the following system schematic, each component block has reliability as shown. Determine the reliability of the entire system

Explanation / Answer

Number of ways to select 3 out of 10 = C(10,3) = 120

Number of ways to select 1st prize 3 out of 3 = C(3,3) = 1

Probability of 1st prize = 1/120 = 0.008333

For 2nd prize.

Out of 3 drawn , 2 are from 3 holder have and 1 from the 7 holder don't have

Number of ways = C(3,2) * C(7,1) = 3 * 7 = 21

Probability for 2nd prize = 21/120 = 0.1750

Relability is correct.

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