class 12

Math

Algebra

Probability

A box contains $15$green and $10$yellow balls. If $10$balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:

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In a hostel $60%$ of the students read Hindi newspaper, $40%$ read English newspaper and $20%$ read Hindi and English newspapers. A student is selected at random.If he reads English newspaper, what is the probability that he reads Hindi newspaper ?

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $53 $be the probability that he knows the answer and $52 $be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $31 $, what is the probability that the student knows the answer given that he answered it correctly

A dice is thrown twice and the sum of the numbers appearing is observed to be $8$. What is the conditional probability that the number $5$ has appeared at least once ?

A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above values you prefer

Let $XandY$be two events that $P(X)=31 ,P(X|Y)=21 andP(Y|X)=52 $then:$P(Y)=154 $ (b) $P(X∪Y)=52 $$P(X_{prime}|Y)=21 $ (d) $P(X∩Y)=51 $

A black and a red dice are rolled.(a) Find the conditional probability of obtaining a sum greater than 9. Given that the black die resulted in a 5.(b) Find the conditional probability of obtaining the sum 8? given that the red die resulted in a number less than 4.

From the set of numbers 1 to 11 two number are taken such that their sum is eve, then the conditional probability that selected numbers are even is equal to (A) $73 $ (B) $53 $ (C) $75 $ (D) $52 $

Two different dice are tossed together. Find the probability (i) of getting a doublet(ii)of getting a sum of 10, of the numbers on two dice