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

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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.


A bag X contains 4 white balls and 2 black balls, while another bag Y contains 3 white balls and 3 black balls. Two balls are drawn (without replacement) at random from one of the bags and were found to be one white and one black. Find the probability that the balls were drawn from bag Y.


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)


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 and B are two events such that P (A) ≠ 0. Find P (B|A), if  A is a subset of B.


A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.


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.


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? 


An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third ball is drawn is black.


Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white ·and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up the box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball is drawn is white, what is the probability that the dice had turned up with a red face?


If events A and B are independent, such that `P(A)= 3/5`,  `P(B)=2/3` 'find P(A ∪ B).


Bag A contains 4 white balls and 3 black balls. While Bag B contains 3 white balls and 5 black balls. Two balls are drawn from Bag A and placed in Bag B. Then, what is the probability of drawing a white ball from Bag B?


In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.


From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when first card drawn is kept aside


From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack


Three fair coins are tossed. What is the probability of getting three heads given that at least two coins show heads?


If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent


A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that the problem is solved?


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 the oil had to be changed, what is the probability that a new oil filter is needed?


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?


Choose the correct alternative:

If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is


In a multiple-choice question, there are three options out of which only one is correct. A person is guessing the answer at random. If there are 7 such questions, then the probability that he will get exactly 4 correct answers is ______ 


If X denotes the number of ones in five consecutive throws of a dice, then P(X = 4) is ______ 


The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______ 


Three machines E1, E2, E3 in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.


If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.


If P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.


If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to ______.


A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and without noticing its colour is placed in the second bag. If a ball is drawn from the second bag, then find the probability that the drawn ball is red in colour.


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 ______.


Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?


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?

Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.


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