English

Let A and B be two independent events. Then P(A ∩ B) = P(A) + P(B)

Advertisements
Advertisements

Question

Let A and B be two independent events. Then P(A ∩ B) = P(A) + P(B)

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is False.

Explanation:

Because P(A ∩ B) = P(A).P(B)

When events 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 20 | Page 271

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

If A and B are two independent events such that `P(barA∩ B) =2/15 and P(A ∩ barB) = 1/6`, then find P(A) and P(B).


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.

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).


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)

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`).


In a race, the probabilities of A and B winning the race are `1/3` and `1/6` respectively. Find the probability of neither of them winning the race.


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, exactly two students solve the problem?


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 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, the balls are of different 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:

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:

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)


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.


Refer to Question 1 above. If the die were fair, determine whether or not the events A and B 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"("B"/"A")`


If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.


If A and B are such events that P(A) > 0 and P(B) ≠ 1, then P(A′|B′) equals ______.


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 independent events are always mutually exclusive.


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


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’


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


If A, B are two events such that `1/8 ≤ P(A ∩ B) ≤ 3/8` then


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.


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 ______.


Let E and F be two independent events. The probability that both E and F happen is `1/12` and the probability that neither E nor F happens is `1/2`, then a value of `(P(E))/(P(F))` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×