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 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.


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


Let E and F be events with `P(E) = 3/5, P(F) = 3/10 and P(E ∩ F) = 1/5`.  Are E and F independent?


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 king or queen’

F : ‘the card drawn is a queen or jack’


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


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?


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?


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 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 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?


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.


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:

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 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 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 = ______.


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


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")`


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")`


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: P1P2 


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 ______.


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


Two independent events are always mutually exclusive.


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

F : ‘the card drawn is a king’


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


Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.


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 ______.


Let EC denote the complement of an event E. Let E1, E2 and E3 be any pairwise independent events with P(E1) > 0 and P(E1 ∩ E2 ∩ E3) = 0. Then `"P"(("E"_2^"C"  ∩ "E"_3^"C")/"E"_1)` is equal to ______.


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


A die is thrown once. What is the sample space \[S\]?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×