Probability

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #81

If `\bar{A}` and `\bar{B}` are the events complementary to the events `A` & `B` respectively, then prove that `P(\bar{A}\ \text{or}\ \bar{B}) = 1 - P(A) P(B | A)`

Question No: #82

Show that the probability of occurring exactly one events between `A` & `B` is `P(A) + P(B) - 2P(AB)`

Question No: #83

`A, B` & `C` are three events such that `P(C) = 0.55`, `P(A | C) = 0.25`, `P(B | C) = 0.4` and `P(A \cap B \cap C) = 0.30` then find `P((A \cup B) | C))`
Ans: 0.1045
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Question No: #84

`A, B, C` are three events such hat `P(B) = 3/4`, `P(A^c \cap B \cap C^c) = 1/3` and `P(A \cap B \cap C^c) = 1/3`, then the value of `P(B \cap C)` is -
(a) `1/12`, (b) `5/12`, (c) `1/4`, (d) `23/36`
Ans: (a) `1/12`
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Question No: #85

Two events `A` & `B` are such that that `P(A^c) = 0.3`, `P(B) = 0.4` and `P(A \cap B^c) = 0.5`. Then find `P(B | A \cup B^c)`
Ans: `1/4`
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Question No: #86

If `P(A) = 0.8`, `P(A | B) = 0.8` and `P(A \cap B) = 0.5`, then find `P(A \cap B | \bar{B})`
Ans: `0`
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Question No: #87

The probability that a teacher will give an unannounced test during any class meeting is `1/5`. If a student is absent twice, then find the probability that the student will miss at least one test.
Ans: `9/25`
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Question No: #88

The probability that a contractor will get a contract `A` is `3/5` and contract `B` is `1/3`; and the probability of getting both contracts is `1/8`. What is the probability that the contractor will get one contract between A or B?
Ans: `97/120`
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Question No: #89

12 cards, numbered 1 to 12, are placed in a box, mixed up thoroughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number.
Ans: `5/9`
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Question No: #90

A couple has 2 children. Find the probability that both are boys, if it is known that --
(i) one of them is a boy,
(ii) the older child is a boy.
Ans: (i) `1/3`, (ii) `1/2`
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