English

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

Advertisements
Advertisements

Question

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

Fill in the Blanks
Advertisements

Solution

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

Explanation:

P(A′ ∪ B) = 1 – P(A ∩ B′)

= 1 – P(A) P(B′)  ......(since A and B′ are independent).

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 19 | Page 271

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

A speaks truth in 60% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A?


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


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.

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)

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'.


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?


The probabilities of solving a specific problem independently by A and B are `1/3` and `1/5` respectively. If both try to solve the problem independently, find the probability that the problem is solved.


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, exactly two students solve the problem?


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 at least one of them 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

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


Solve the following:

If P(A ∩ B) = `1/2`, P(B ∩ C) = `1/3`, P(C ∩ A) = `1/6` then find P(A), P(B) and P(C), If A,B,C are independent events.


Solve the following:

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


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(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"("B'"/"A")`


Solve the following:

A and B throw a die alternatively till one of them gets a 3 and wins the game. Find the respective probabilities of winning. (Assuming A begins the game)


Solve the following:

Consider independent trails consisting of rolling a pair of fair dice, over and over What is the probability that a sum of 5 appears before sum of 7?


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.


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"("B"/"A")`


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').


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: 1 – (1 – P1)(1 – P2) 


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


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


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 ______.


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)


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 ______.


A problem in Mathematics is given to three students whose chances of solving it are `1/2, 1/3, 1/4` respectively. If the events of their solving the problem are independent then the probability that the problem will be solved, is ______.


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


What are independent events in probability?


For \[E=\{3,6\}\] and \[F=\{2,4,6\}\], what is \[E\cap F\]?


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


Which statement correctly distinguishes mutually exclusive events and independent events?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×