मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

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 eve

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • `52/96`

  • `71/96`

  • `69/96`

  • `13/96`

MCQ
Advertisements

उत्तर

`71/96`

Explanation;

[Hint : Required probability = `1 - 5/8 xx 5/12`

= `1 - 25/96 = 71/96`]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Probability - Miscellaneous Exercise 9 [पृष्ठ २१३]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 1 [English] Standard 11 Maharashtra State Board
पाठ 9 Probability
Miscellaneous Exercise 9 | Q I. (10) | पृष्ठ २१३

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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?


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.

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’


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.


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.


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 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?


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

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?


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


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)


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


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


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")`


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 


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 – P1) P2 


A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P(B′ ∩ A) equals ______.


If two events are independent, then ______.


Let A and B be two events such that P(A) = `3/8`, P(B) = `5/8` and P(A ∪ B) = `3/4`. Then P(A|B).P(A′|B) is equal to ______.


If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then P(At least two of A, B, C occur) = 3p2 – 2p3 


Let A and B be two events. If P(A | B) = P(A), then A is ______ of 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’


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


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.


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.


Five fair coins are tossed simultaneously. The probability of the events that at least one head comes up is ______.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×