Q5. An urn contains 4 red and 6 white chips, 5 chips are drawn at random, without replacement. a. What is the probability that the first three chip flow exactly the sequence RWR? b. What is the probability that the second chip is red? c. hat is probability of drawing a total of 2 red chips out of the 5?

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Q6. 

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09:48
Assignment-4 (1).pdf
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MT 207
PROBABILITY THEORY
ASSIGNMENT 3
Q1. Given group of 6 computer engineer, 7 mechanical engineer and 8 civil engineer
a. How many teams of 5 members can be formed?
b. How many with exactly 3 Computer Engineers?
c. How many 10-member teams with 3 computer engineer,2 mechanical engineer and
5 civil engineer?
Q2. Four married couples sit in a row. In how many ways can this be done if
a. There are no restrictions.
b. Each married couple sits together.
Q3. Suppose that Pis a probability measure defined on the sample space S. Prove that
P(A°OB° )=1-P(A)– P(B)+P(A^B).
Q4. Let A and B be events with P(A)=0.3, P(AUB)=0.5and P(B) = p.
Find pif:
a. .A and Bare disjoint.
b. A and Bare independent.
Q5. An urn contains 4 red and 6 white chips, 5 chips are drawn at random, without replacement.
a. What is the probability that the first three chip flow exactly the sequence RWR?
b. What is the probability that the second chip is red?
c. hat is probability of drawing a total of 2 red chips out of the 5?
d. Answer the previous question if they are drawn with replacement.
Q6. Dr. Lawrence has three boxes. Their contents are
Box 1: 2 red balls and 4 white balls
Box 2: 4 red balls and 2 white balls
Box 3: 3 red balls and 3 white balls
First, a box is selected, and then two balls are drawn at random from that box (without
replacement).
a. What is the probability that the selected both balls are of the same color.
b. If the selected balls are of the same color, what is the probability that they are selected
from box 2?
Transcribed Image Text:09:48 Assignment-4 (1).pdf + MT 207 PROBABILITY THEORY ASSIGNMENT 3 Q1. Given group of 6 computer engineer, 7 mechanical engineer and 8 civil engineer a. How many teams of 5 members can be formed? b. How many with exactly 3 Computer Engineers? c. How many 10-member teams with 3 computer engineer,2 mechanical engineer and 5 civil engineer? Q2. Four married couples sit in a row. In how many ways can this be done if a. There are no restrictions. b. Each married couple sits together. Q3. Suppose that Pis a probability measure defined on the sample space S. Prove that P(A°OB° )=1-P(A)– P(B)+P(A^B). Q4. Let A and B be events with P(A)=0.3, P(AUB)=0.5and P(B) = p. Find pif: a. .A and Bare disjoint. b. A and Bare independent. Q5. An urn contains 4 red and 6 white chips, 5 chips are drawn at random, without replacement. a. What is the probability that the first three chip flow exactly the sequence RWR? b. What is the probability that the second chip is red? c. hat is probability of drawing a total of 2 red chips out of the 5? d. Answer the previous question if they are drawn with replacement. Q6. Dr. Lawrence has three boxes. Their contents are Box 1: 2 red balls and 4 white balls Box 2: 4 red balls and 2 white balls Box 3: 3 red balls and 3 white balls First, a box is selected, and then two balls are drawn at random from that box (without replacement). a. What is the probability that the selected both balls are of the same color. b. If the selected balls are of the same color, what is the probability that they are selected from box 2?
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