हिंदी

Two independent events are always mutually exclusive.

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प्रश्न

Two independent events are always mutually exclusive.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

This statement is False.

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अध्याय 13: Probability - Exercise [पृष्ठ २८५]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 13 Probability
Exercise | Q 97 | पृष्ठ २८५

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.


If A and B are two events such that `P(A) = 1/4, P(B) = 1/2 and P(A ∩ B) = 1/8`, find P (not A and not B).


Events A and B are such that `P(A) = 1/2, P(B) = 7/12 and P("not A or not B") = 1/4` . State whether A and B are independent?


Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find 

  1. P (A and B)
  2. P(A and not B)
  3. P(A or B)
  4. P(neither A nor B)

Prove that if E and F are independent events, then the events E and F' are also independent. 


A speaks the truth in 60% of the cases, while B is 40% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?


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?


A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, problem is not solved


The probability that a 50-year old man will be alive till age 60 is 0.83 and the probability that a 45-year old woman will be alive till age 55 is 0.97. What is the probability that a man whose age is 50 and his wife whose age is 45 will both be alive after 10 years?


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.


The probability that a student X solves a problem in dynamics is `2/5` and the probability that student Y solves the same problem is `1/4`. What is the probability that

  1. the problem is not solved
  2. the problem is solved
  3. the problem is solved exactly by one of them

The probability that a man who is 45 years old will be alive till he becomes 70 is `5/12`. The probability that his wife who is 40 years old will be alive till she becomes 65 is `3/8`. What is the probability that, 25 years hence,

  1. the couple will be alive
  2. exactly one of them will be alive
  3. none of them will be alive
  4. at least one of them will be alive

A family has two children. Find the probability that both the children are girls, given that atleast one of them is a girl.


Solve the following:

If P(A) = `"P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3` the find `"P"("A'"/"B")`


Solve the following:

Let A and B be independent events with P(A) = `1/4`, and P(A ∪ B) = 2P(B) – P(A). Find `"P"("A"/"B")`


10% of the bulbs produced in a factory are of red colour and 2% are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.


Two dice are thrown together. Let A be the event ‘getting 6 on the first die’ and B be the event ‘getting 2 on the second die’. Are the events A and B independent?


A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A'"/"B'")`


Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: P1 + P2 – 2P1P2 


Two dice are tossed. Find whether the following two events A and B are independent: A = {(x, y): x + y = 11} B = {(x, y): x ≠ 5} where (x, y) denotes a typical sample point.


If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals ______.


If A and B are two independent events with P(A) = `3/5` and P(B) = `4/9`, then P(A′ ∩ B′) equals ______.


If A and B are two independent events then P(A and B) = P(A).P(B).


If A and B are independent, then P(exactly one of A, B occurs) = P(A)P(B') + P(B)P(A') 


If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then P(B|A) ≥ `1 - ("P"("B'"))/("P"("A"))`


If A and B are two events such that P(A|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.


Two events 'A' and 'B' are said to be independent if


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


Events A and Bare such that P(A) = `1/2`, P(B) = `7/12` and `P(barA ∪ barB) = 1/4`. Find whether the events A and B are independent or not.


The probability that A hits the target is `1/3` and the probability that B hits it, is `2/5`. If both try to hit the target independently, find the probability that the target is hit.


Given two independent events, if the probability that exactly one of them occurs is `26/49` and the probability that none of them occurs is `15/49`, then the probability of more probable of the two events is ______.


If E and F are independent, which pair is also independent?


A die is thrown once. If F is the event that the number appearing is even, which set represents F?


For \[E\cap F=\{6\}\] when a die is thrown once, what is \[P(E\cap F)\]?


For \[P(E)=\frac{1}{3}\] and \[P(F)=\frac{1}{2}\], what is \[P(E)P(F)\]?


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