Use the data in the accompanying table to answer the following questions. Expres

Question

Use the data in the accompanying table to answer the following questions. Express the probability as decimal numbers (round to 4 decimal places). Show your work! a) If one of the 1068 subjects is randomly selected, find the probability of selecting someone sentenced to prison. b) If one of the 1068 subjects is randomly selected, find the probability of selecting someone not sentenced to prison. c) Find the probability of being sentenced to prison, given that the subject entered a plea of guilty. d) Find the probability of being sentenced to prison, given that the subject entered a plea of not guilty. e) If 1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison or entered a plea of guilty. f) If 2 different subjects are randomly selected, find the probability that they both were sentenced to prison. g) If 2 different subjects are randomly selected, find the probability that they both entered pleas of not guilty. h) If 1 of the subjects is randomly selected, find the probability of selecting someone who entered a plea of not guilty or was not sentenced to prison. i) If 1 of the subjects is randomly selected, find the probability of selecting someone who was sentenced to prison and entered a plea of guilty. j) If 1 of the subjects is randomly selected, find the probability of selecting someone who was not sentenced to prison and did not enter a plea of guilty.

Explanation / Answer

2. a) P(Selecting someone sentenced to prison)

= (402 + 68) / 1068

= 470 / 1068

= 0.44

b) P(Selecting someone not sentenced to prison)

= 1 - P(Selecting someone sentenced to prison)

= 1 - 0.44 [From part a)]

= 0.56

c) P(Sentenced to prison | entered a plea of gulity)

= 402 / (402 + 574)

= 402 / 976

= 0.41

d) P(Sentenced to prison | entered a plea of not gulity)

= 68 / (68 + 24)

= 68 / 92

= 0.74

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