Determine the probability p, or an estimate of it, for each of the following eve

Question

Determine the probability p, or an estimate of it, for each of the following events: (a) A king, ace, jack of clubs, or queen of diamonds appears in drawing a single card from a well-shuffled ordinary' deck of cards. (b) The sum 8 appears in a single toss of a pair of fair dice. (c) A nondefective bolt will be found if out of 600 bolts already examined, 12 were defective, (id) A 7 or 11 comes up in a single toss of a pair of fair dice. (e) At least one head appears in three losses of a fair coin.

Explanation / Answer

a. Number of kings, aces, jack of clubs and queen of diamonds in a deck = 4 + 4 + 1 + 1 = 10

Cards in a deck = 52

p = 10 / 52 = 0.1923

b. No. of ways in which sum is 8 = {(2,6) , (3,5) , (4,4) , (5,3) , (6,2)} = 5

Total no. of ways = 36

p = 5/36 = 0.1389

c. No. of non defectives = 600-12 = 588

p = (600-12) / 600 = 0.98

d. No. of ways in which sum is 7 or 11 : {(1.6) . (6,1) , (2,5) , (5,2) , (3,4) , (4,3) , (5,6) , (6,5)} = 8

p = 8/36 = 0.2222

e. P(At least one head) = 1 - P(No head) = 1 - 0.53 = 0.875

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