Question

a. In rolling 3 fair dice, what is the probability of obtaining a sum not greater than 16?

b. In rolling 2 fair dice, what is the probability of a sum greater than 3 but not exceeding 6?

c. If a box contains 10 left-handed and 20 right-handed screws, what is the probability of obtaining at least one right-handed screw in drawing 2 screws with replacement?

d. Will the probability in Prob. 5 increase or decrease if we draw without replacement. First guess, then calculate.

e. If we inspect photocopy paper by randomly drawing 5 sheets without replacement from every pack of 500, what is the probability of getting 5 clean sheets although of the sheets contain spots?

f. Suppose that we draw cards repeatedly and with replacement from a file of 100 cards, 50 of which refer to male and 50 to female persons. What is the probability of obtaining the second “female” card before the third “male” card?

g. A batch of 200 iron rods consists of 50 oversized rods, 50 undersized rods, and 100 rods of the desired length. If two rods are drawn at random without replacement, what is the probability of obtaining (a) two rods of the desired length, (b) exactly one of the desired length, (c) none of the desired length?

Answer 1

a) Required probability is equal to 1-probability that sum is greater than 16.

Now the sum is greater than 16 if outcomes are

So it's probability is

Hence the required probability is

b) The sum is greater than 3 and less than 6 in the following case

Hence the required probability is

c) Total number of Screws is 10+20=30

Number of ways in which 2 can be drawn from 30 is

Required probability is equal to 1-probability of no screw is right handed (that's both are left handed)

Probability that both are left handed is

Hence the required probability is