मराठी

Two independent events are always mutually exclusive. - Mathematics

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प्रश्न

Two independent events are always mutually exclusive.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

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 97 | 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.


Two events, A and B, will be independent if ______.


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?


One-shot is fired from each of the three guns. Let A, B, and C denote the events that the target is hit by the first, second and third guns respectively. assuming that A, B, and C are independent events and that P(A) = 0.5, P(B) = 0.6, and P(C) = 0.8, then find the probability that at least one hit is registered.


The odds against a certain event are 5: 2 and odds in favour of another independent event are 6: 5. Find the chance that at least one of the events will happen.


The odds against student X solving a business statistics problem are 8: 6 and odds in favour of student Y solving the same problem are 14: 16 What is the chance that the problem will be solved, if they try independently?


The odds against student X solving a business statistics problem are 8: 6 and odds in favour of student Y solving the same problem are 14: 16 What is the probability that neither solves the problem?


A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are `3/4, 1/2` and `5/8`. Find the probability that the target

  1. is hit exactly by one of them
  2. is not hit by any one of them
  3. is hit
  4. is exactly hit by two of them

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 follwoing 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 that the person was satisfied given that the person had Throat surgery.


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.


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?


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


Select the correct option from the given alternatives :

The odds against an event are 5:3 and the odds in favour of another independent event are 7:5. The probability that at least one of the two events will occur is


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.


If A and B are independent events such that 0 < P(A) < 1 and 0 < P(B) < 1, then which of the following is not correct?


If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of A, B) = `5/9`, then p = ______.


Two dice are thrown together and the total score is noted. The events E, F and G are ‘a total of 4’, ‘a total of 9 or more’, and ‘a total divisible by 5’, respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are 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")`


If A and B are two events and A ≠ Φ, B ≠ Φ, then ______.


In Question 64 above, P(B|A′) is equal to ______.


Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E|F) – P(F|E) equals ______.


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


If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P(At least two of A, B, C occur) = 3p2 – 2p3 


One card is drawn at random from a well-shuffled deck of 52 cards. In which of the following case is the events E and F independent?

E : ‘the card drawn is a spade’

F : ‘the card drawn is an ace’


The probability of obtaining an even prime number on each die when a pair of dice is rolled is


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


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 of the event A occurring is `1/3` and of the event B occurring is `1/2`. If A and B are independent events, then find the probability of neither A nor B occurring.


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