This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on "Baye's Theorem".

IF IM NOT SATISFIED WITH YOUR ANSWER, I WILL RATE UNHELPFUL. Im just being honest here

1. Three companies A, B and C supply 25%, 35% and 40% of the notebooks to a school. Past experience shows that 5%, 4% and 2% of the notebooks produced by these companies are defective. If a notebook was found to be defective, what is the probability that the notebook was supplied by A?

a)4469

b)2569

c)1324

d)1124

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2. A box of cartridges contains 30 cartridges, of which 6 are defective. If 3 of the cartridges are removed from the box in succession without replacement, what is the probability that all the 3 cartridges are defective?

a)(654)

(303030)

b)(654)

(302928)

c)(653)

(302928)

d)(666)

(303030)

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3. Two boxes containing candies are placed on a table. The boxes are labelled B1and B2. Box B1contains 7 cinnamon candies and 4 ginger candies. Box B2contains 3 cinnamon candies and 10 pepper candies. The boxes are arranged so that the probability of selecting box B1is13and the probability of selecting box B2is23. Suresh is blindfolded and asked to select a candy. He will win a colour TV if he selects a cinnamon candy. What is the probability that Suresh will win the TV (that is, she will select a cinnamon candy)?

a)733

b)633

c)1333

d)2033

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4. Two boxes containing candies are placed on a table. The boxes are labelled B1and B2. Box B1contains 7 cinnamon candies and 4 ginger candies. Box B2contains 3 cinnamon candies and 10 pepper candies. The boxes are arranged so that the probability of selecting box B1is13and the probability of selecting box B2is23. Suresh is blindfolded and asked to select a candy. He will win a colour TV if he selects a cinnamon candy. If he wins a colour TV, what is the probability that the marble was from the first box?

a)713

b)137

c)733

d)633

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5. Suppose box A contains 4 red and 5 blue coins and box B contains 6 red and 3 blue coins. A coin is chosen at random from the box A and placed in box B. Finally, a coin is chosen at random from among those now in box B. What is the probability a blue coin was transferred from box A to box B given that the coin chosen from box B is red?

a)1529

b)1429

c)12

d)710

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6. An urn B1contains 2 white and 3 black chips and another urn B2contains 3 white and 4 black chips. One urn is selected at random and a chip is drawn from it. If the chip drawn is found black, find the probability that the urn chosen was B1.

a)47

b)37

c)2041

d)2141

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7. At a certain university, 4% of men are over 6 feet tall and 1% of women are over 6 feet tall. The total student population is divided in the ratio 3:2 in favour of women. If a student is selected at random from among all those over six feet tall, what is the probability that the student is a woman?

a)25

b)35

c)311

d)1100

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8. Previous probabilities in Bayes Theorem that are changed with help of new available information are classified as _________________

a) independent probabilities

b) posterior probabilities

c) interior probabilities

d) dependent probabilities