हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • P(A|B) = P(A).P(B)

  • P(A|B) = `("P"("A" ∩ "B"))/("P"("B"))`

  • P(A|B).P(B|A)=1

  • P(A|B) = P(A)|P(B)

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

If A and B are two events and A ≠ Φ, B ≠ Φ, then P(A|B) = `("P"("A" ∩ "B"))/("P"("B"))`.

Explanation:

Given that: A ≠ Φ and B ≠ Φ

Then P(A|B) = `("P"("A" ∩ "B"))/("P"("B"))`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 13: Probability - Exercise [पृष्ठ २८०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 13 Probability
Exercise | Q 62 | पृष्ठ २८०

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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.

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

  1. P (A ∩ B)
  2. P (A ∪ B)
  3. P (A | B)
  4. P (B | A)

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.

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


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`).


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


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?


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, 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, problem is not solved


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.


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 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 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`


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


Solve the following:

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


Solve the following:

For three events A, B and C, we know that A and C are independent, B and C are independent, A and B are disjoint, P(A ∪ C) = `2/3`, P(B ∪ C) = `3/4`, P(A ∪ B ∪ C) = `11/12`. Find P(A), P(B) and P(C)


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?


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"("B"/"A")`


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


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 


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 ______.


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


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


Two independent events are always mutually exclusive.


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


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"))`


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’


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


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.


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.


Two players A and B are alternately throwing a coin and a die together. A player who first throws head and 6 wins the game. If A starts the game, then the probability that B wins the game is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×