English

Three events A, B and C are said to be independent if P(A ∩ B ∩ C) = P(A) P(B) P(C).

Advertisements
Advertisements

Question

Three events A, B and C are said to be independent if P(A ∩ B ∩ C) = P(A) P(B) P(C).

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is False.

Explanation:

Reason is that A, B, C will be independent if they are pairwise independent and P(A ∩ B ∩ C) = P(A) P(B) P(C).

shaalaa.com
  Is there an error in this question or solution?
Chapter 13: Probability - Solved Examples [Page 271]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 13 Probability
Solved Examples | Q 21 | Page 271

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.


A bag contains 4 balls. Two balls are drawn at random (without replacement) and are found to be white. What is the probability that all balls in the bag are white?


Given that the events A and B are such that `P(A) = 1/2, PA∪B=3/5 and P (B) = p`. Find p if they are

  1. mutually exclusive
  2. independent.

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?


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.

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?


If P(A) = 0·4, P(B) = p, P(A ⋃ B) = 0·6 and A and B are given to be independent events, find the value of 'p'.


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 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

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 person was unsatisfied given that the person had eye surgery


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

Solve the following:

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


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")`


Solve the following:

A machine produces parts that are either good (90%), slightly defective (2%), or obviously defective (8%). Produced parts get passed through an automatic inspection machine, which is able to detect any part that is obviously defective and discard it. What is the quality of the parts that make it throught the inspection machine and get shipped?


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?


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 = ______.


If A and B′ are independent events then P(A′ ∪ B) = 1 – ______.


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")`


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'")`


Three events A, B and C have probabilities `2/5, 1/3` and `1/2`, , respectively. Given that P(A ∩ C) = `1/5` and P(B ∩ C) = `1/4`, find the values of P(C|B) and P(A' ∩ C').


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.


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


If A and B are mutually exclusive events, then they will be independent also.


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|B) = p, P(A) = p, P(B) = `1/3` and P(A ∪ B) = `5/9`, then p = ______.


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 black’

F : ‘the card drawn is a king’


Let E1 and E2 be two independent events. Let P(E) denotes the probability of the occurrence of the event E. Further, let E'1 and E'2 denote the complements of E1 and E2, respectively. If P(E'1 ∩ E2) = `2/15` and P(E1 ∩ E'2) = `1/6`, then P(E1) is


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


Let Bi(i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is α, only B2 occurs is β and only B3 occurs is γ. Let p be the probability that none of the events Bi occurs and these 4 probabilities satisfy the equations (α – 2β)p = αβ and (β – 3γ) = 2βy (All the probabilities are assumed to lie in the interval (0, 1)). Then `("P"("B"_1))/("P"("B"_3))` is equal to ______.


Given two events A and B such that (A/B) = 0.25 and P(A ∩ B) = 0.12. The value P(A ∩ B') is ______.


Two events E and F are independent when which conditional probability condition holds, provided \[P(E) \ne 0\]?


Two events E and F are independent when which conditional probability condition holds, provided \[P(F) \ne 0\]?


For independent events A and B, what is the probability that at least one occurs?


Which statement correctly distinguishes mutually exclusive events and independent events?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×