1. Calculate the probability of each of the following events. (4 points) a. At l

Question

1. Calculate the probability of each of the following events. (4 points) a. At least one head comes up in a sequence of four flips of a coin b. For a die that is 3 times as likely to land on 1, 5, or 6 as it is to land on 2, 3, or 4 calculate the probability of rolling an odd number. In a lottery where four digits are randomly selected with replacement and any permutation of the matching numbers means you win, find the probability of winning if you select the number 1, 1, 5,0 c. d. In the same lottery as part c, suppose you instead select the number 3, 4, 5,1

Explanation / Answer

a) P(at least one head) = 1 - P(all tails)

= 1 - 0.54

= 0.9375

b) Let, P(2) = P(3) = P(4) = p

P(1) = P(5) = P(6) = 3p

3x3p + 3xp = 1

12p = 1

p = 1/12

P(odd number) = P(1) + P(3) + P(5)

= 3/12 + 1/12 + 3/12

= 7/12

c) P(1,1,5,0) = (1/10)4 x 4!/(2!)

= 0.0012

d) P(3,4,5,1) = (1/10)4 x 4!

= 0.0012

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