मराठी

Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent. - Mathematics

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प्रश्न

Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.

पर्याय

  • True

  • False

MCQ
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उत्तर

This statement is False.

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पाठ 13: Probability - Exercise [पृष्ठ २८५]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 13 Probability
Exercise | Q 94 | पृष्ठ २८५

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

If `P(A)  = 3/5 and P(B) = 1/5` , find P (A ∩ B) if A and B are independent events.


Let A and B be independent events with P (A) = 0.3 and P (B) = 0.4. Find 

  1. P (A ∩ B)
  2. P (A ∪ B)
  3. P (A | B)
  4. P (B | A)

Probability of solving specific problem independently by A and B are `1/2` and `1/3` respectively. If both try to solve the problem independently, find the probability that

  1. the problem is solved
  2. exactly one of them solves the problem.

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability `1/2`).


A fair die is rolled. If face 1 turns up, a ball is drawn from Bag A. If face 2 or 3 turns up, a ball is drawn from Bag B. If face 4 or 5 or 6 turns up, a ball is drawn from Bag C. Bag A contains 3 red and 2 white balls, Bag B contains 3 red and 4 white balls and Bag C contains 4 red and 5 white balls. The die is rolled, a Bag is picked up and a ball is drawn. If the drawn ball is red; what is the probability that it is drawn from Bag B?


An urn contains four tickets marked with numbers 112, 121, 122, 222 and one ticket is drawn at random. Let Ai (i = 1, 2, 3) be the event that ith digit of the number of the ticket drawn is 1. Discuss the independence of the events A1, A2, and A3.


The odds against a husband who is 55 years old living till he is 75 is 8: 5 and it is 4: 3 against his wife who is now 48, living till she is 68. Find the probability that the couple will be alive 20 years hence.


Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery.

The following table summarizes their response:

Surgery Satisfied Unsatisfied Total
Throat 70 25 95
Eye 90 15 105
Total 160 40 200

If one person from the 200 patients is selected at random, determine the probability the person had Throat surgery given that the person was unsatisfied.


A bag contains 3 yellow and 5 brown balls. Another bag contains 4 yellow and 6 brown balls. If one ball is drawn from each bag, what is the probability that, both the balls are of the same color?


Bag A contains 3 red and 2 white balls and bag B contains 2 red and 5 white balls. A bag is selected at random, a ball is drawn and put into the other bag, and then a ball is drawn from that bag. Find the probability that both the balls drawn are of same color


A bag contains 3 red and 5 white balls. Two balls are drawn at random one after the other without replacement. Find the probability that both the balls are white.

Solution: Let,

A : First ball drawn is white

B : second ball drawn in white.

P(A) = `square/square`

After drawing the first ball, without replacing it into the bag a second ball is drawn from the remaining `square` balls.

∴ P(B/A) = `square/square`

∴ P(Both balls are white) = P(A ∩ B)

`= "P"(square) * "P"(square)`

`= square * square`

= `square`


Solve the following:

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Solve the following:

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The probability of simultaneous occurrence of at least one of two events A and B is p. If the probability that exactly one of A, B occurs is q, then prove that P(A′) + P(B′) = 2 – 2p + q.


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If two events are independent, then ______.


If the events A and B are independent, then P(A ∩ B) is equal to ______.


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Two independent events are always mutually exclusive.


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