Question

Statistics

EXERCISE 17. A die is cast three times. What is the probability a) of not getting three 6´s in succession? b) that the same number appears three times? Answer. a) 215/216. b) 6/216.

EXERCISE 18. A die is thrown three times. What is the probability a) that the sum if the three faces shown is either 3 or 4? b) that the sum if the three faces shown is greater than 4? Answer. a) 4/216. b) 212/216.

EXERCISE 19. A hunter fires 7 consecutive bullets at an angry tiger. If the probability that 1 bullet will kill is 60%, what is the probability that the hunter is still alive? Answer. 99,83616%.

EXERCISE 20. According to the U. S. Census Bureau, 62% of Americans over the age of 18 are married. Find the probability of getting two married people (not necessarily to each other) when two different Americans over the age of 18 are randomly selected. Answer. 38,4%.

EXERCISE 21. A Roper poll showed that 18% of adults regularly engage in swimming. If three adults are randomly selected, find the probability that they all regularly engage in swimming. Answer. 0,583%.

EXERCISE 22. Four firms using the same auditor independently and randomly select a month in which to conduct their annual audits. What is the probability that all four months are different? Answer. 55/96.

Please show your workings. I have provide you with the possible answers. Some of them might be wrong though. If there is not gonna be enough space you can show your working on a picture. Thank you in advance!

Answer 1

soltion:

if a die is rolled three times , then total number of outcomes = 6 * 6 * 6 * = 216

a) P(not getting 3 six's on three rolls) = 1 - P(getting 3 six's on the three rolls)

P(getting 3 six's on the three rolls) = (1 / 6 ) * (1 / 6) * (1 / 6) = 1/216

P(not getting 3 six's on three rolls) = 1 - 1/216 = 215/216

b) P(same number appear three times) = P(getting three one's)+P(getting 3 two's) + P(three 3's) + P(three 4's) + P(three 5's) = P(three 6's)

probability of getting three same numbers =

18) a) getting a sum of 3 or 4 on rolling a die three times

getting a sum of 3 can be if three times one appear on the die,

so, P(getting a sum of three) = 1/6 * 1/6 * 1/6 = 1/216

getting a sum of four may come in three ways = (1+1+2) or (1 + 2 + 1) or (2 + 1 + 1)

so probability of getting a sum of 4 = 3/216

P(getting a sum of 3 or 4) = 1/216 + 3 / 216 = 4/216

b) P( sum of three face greater than 4) = 1 - P(sum of three faces 3 or 4)

P( sum of three face greater than 4) = 1 - 4/216 = 212/216

19) total bulets fired n = 7

probability of killing by one bullet p = 0.6

probability that the hunter is alive means the probability that tiger is killed

so, P(hunter alive) = P(tiger is killed)

P(tiger killed) = 1 - P(tiger is not killed)

using bionomial formula

tiger is not killed means no bullet kill the tiger

so

P(hunter alive) = P(tiger is killed) = 1 - 0.0016384 = 0.9983616 = 99.83616%

20) probability of married (p) = 0.62

n = 2

using binomial formula

probability that 2 out of 2 selected american are married =0.3844 = 38.4%