2. Let A and B be events in the sample space S, and let Pr[A] = 0.38, Pr[B] = 0.
ID: 3130388 • Letter: 2
Question
2. Let A and B be events in the sample space S, and let Pr[A] = 0.38, Pr[B] = 0.68, and Pr[AB] = 0.11. Find the probability of each of the following events.
a) Pr[AB] =
b) Pr[AB] =
c) Pr[AB] =
6. Suppose E, F, and G are events in a sample space S, with Pr[E] = 0.29, Pr[F] = 0.42,
Pr[G] =0.55, Pr[EF] = 0.49, Pr[EG] = 0.12, and Pr[FG] =0.24. Find the following probability.
Pr[EG]=
7. Suppose E, F, and G are events in a sample space S, with Pr[E] = 0.58, Pr[F] = 0.25,
Pr[G] =0.38, Pr[EF] = 0.62, Pr[EG] = 0.24, and Pr[FG] =0.47. Find the following probability.
Pr[G’E] =
8. Let A, B, and C be events which form a partition of a sample space S, and suppose that Pr[A] = 5Pr[B] and Pr[C] = 3Pr[A]. Find each of the following probabilities.
a) Pr[C] =
b) Pr[BC]=
c). Pr[BC] =
9. Five slips of paper with the number 6 through 10 are placed in a box. After mixing well, two slips are drawn. Write a sample with equally likely outcomes and find the probability of drawing two even numbers, two odd numbers, and an even and an odd number.
Part of the sample space is (6,7),(6,9),(6,10),(7,9),(7,10),(8,10),(9,10)
The missing outcomes are?
10. Each Monday a student attends mathematics class with probability 0.91, skips accounting class with probability 0.44, and attends both with probability 0.53. Find the probability that she attends at least one class on Monday.
Probability =
11. A marble is drawn at random from a box containing 2 yellow, 7 white, and 14 blue marbles. Find the probabilities in parts
a-c
a. A yellow marble is drawn
b. A black marble is drawn
The probability is?
12. In a class of 226 students, there are 112 freshman and 114 sophomores. Of the freshmen, 69 are Indiana residents and of the sophomores 68 are Indiana residents. A student is selected at random from among the members of the class. Find the probability that the student selected is not an Indiana resident.
Probability=
14. A television set which sometimes malfunctions has
Characteristic
Probability
A clear picture
0.63
Good sound
0.52
Good color
0.78
Clear picture and good sound
0.40
Clear picture and good color
0.50
Good sound and good color
0.40
Find the probability that the television set has exactly one of these three characteristics (clear picture, good sound, and good color).
Probability =
15. A survey of 100 people about their music expenditures gave the followinginformation: 34 bought country music, and 29 were professors. Find the following probabilities.
The probability that a person is a professor who bought non-country music is?
Explanation / Answer
2.
a)
Here,
P(A U B) = P(A) + P(B) - P(A n B) = 0.38 + 0.68 - 0.11 = 0.95 [ANSWER]
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b)
Here,
P(A' n B) = P(B) - P(A n B) = 0.68 - 0.11 = 0.57 [ANSWER]
*************
c)
Here,
P(A' n B') = 1 - P(A U B) = 1 - 0.95 = 0.05 [ANSWER]
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