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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct option from the given alternatives : Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags

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प्रश्न

Select the correct option from the given alternatives :

Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II

पर्याय

  • `33/68`

  • `35/69`

  • `34/67`

  • `35/68`

MCQ
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उत्तर

`35/68`

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पाठ 9: Probability - Miscellaneous Exercise 9 [पृष्ठ २१३]

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बालभारती Mathematics and Statistics (Arts and Science) Part 1 [English] Standard 11 Maharashtra State Board
पाठ 9 Probability
Miscellaneous Exercise 9 | Q I. (8) | पृष्ठ २१३

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संबंधित प्रश्‍न

A fair coin is tossed five times. Find the probability that it shows exactly three times head.


A die is thrown three times. Events A and B are defined as below:
A : 5 on the first and 6 on the second throw.
B: 3 or 4 on the third throw.

Find the probability of B, given that A has already occurred.


If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find

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

If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find P(A|B)


If `P(A) = 6/11, P(B) = 5/11 "and"  P(A ∪ B) = 7/11` find

  1. P(A ∩ B)
  2. P(A|B)
  3. P(B|A)

Determine P(E|F).

A coin is tossed three times, where

E: at most two tails, F: at least one tail


A black and a red dice are rolled. 

Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.


A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|G) and P (G|E)


Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.


Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that

  1. both balls are red.
  2. first ball is black and second is red.
  3. one of them is black and other is red.

In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.


A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.


If A and B are events such as that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`, then find

1) P(A / B)

2) P(B / A)


A card is drawn from a well-shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both? 


Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.


 Two balls are drawn from an urn containing 3 white, 5 red and 2 black balls, one by one without replacement. What is the probability that at least one ball is red?


Two cards are drawn one after the other from a pack of 52 cards without replacement. What is the probability that both the cards drawn are face cards?


If P(A) = 0.5, P(B) = 0.8 and P(B/A) = 0.8, find P(A/B) and P(A ∪ B)


If for two events A and B, P(A) = `3/4`, P(B) = `2/5`  and A ∪ B = S (sample space), find the conditional probability P(A/B)


The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If a new oil filter is needed, what is the probability that the oil has to be changed?


One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that one white and one black


Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive


Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events


Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5


A year is selected at random. What is the probability that it contains 53 Sundays


Choose the correct alternative:

If A and B are any two events, then the probability that exactly one of them occur is


A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______


Two dice are thrown. Find the probability that the sum of numbers appearing is more than 11, is ______.


If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:


A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.


If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.


Read the following passage:

Recent studies suggest the roughly 12% of the world population is left-handed.

Depending upon the parents, the chances of having a left-handed child are as follows:

A :  When both father and mother are left-handed:
Chances of left-handed child is 24%.
B :  When father is right-handed and mother is left-handed:
Chances of left-handed child is 22%.
C :  When father is left-handed and mother is right-handed:
Chances of left-handed child is 17%.
D :  When both father and mother are right-handed:
Chances of left-handed child is 9%.

Assuming that P(A) = P(B) = P(C) = P(D) = `1/4` and L denotes the event that child is left-handed.

Based on the above information, answer the following questions:

  1. Find `P(L/C)` (1)
  2. Find `P(overlineL/A)` (1)
  3. (a) Find `P(A/L)` (2)
    OR
    (b) Find the probability that a randomly selected child is left-handed given that exactly one of the parents is left-handed. (2)

If A and B are two independent events such that P(A) = `1/3` and P(B) = `1/4`, then `P(B^'/A)` is ______.


Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each one of them will toss a coin and if one person gets a different result (heads or tails) than the other two, that person would pay. If all three get the same result (all heads or all tails), they will toss again until they get a different result.

  1. What is the probability that all three friends will get the same result (all heads or all tails) in one round of tossing?
  2. What is the probability that they will get a different result in one round of tossing?
  3. What is the probability that they will need exactly four rounds of tossing to determine who would pay?

If A and B are events and \[P(A) \neq 0\], which expression gives \[P(B \mid A)\]?


For a two-child family, let E be “both children are boys” and F be “at least one child is a boy.” Which pair correctly gives E and F?


Which conditional probabilities are equal to 1 when \[P(F)\neq 0\]?


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