List of top Mathematics Questions on Probability asked in CBSE CLASS XII

There are three coins.One is a two headed coin,another is a biased coin that comes up heads \(75\%\) of the and third is an unbiased coin.One of the three coin is chosen at random and tossed,it shows head,what is the probability that it was the two headedcoin?

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''.

If P(A) = \(\frac 12\), P(B) = 0, then P(A|B) is :

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
(i)E:'the card drawn is a spade'
F:'the card drawn is an ace'
(ii)E:'the card drawn is black'
F:'the card drawn is a king'
(iii)E:'the card drawn is a king or queen'
F:'the card drawn is a queen or jack'

If A and B are events such that \(P(A|B)=P(B|A)\), then:

If \(P(A)=\frac 35\) and \(P(B)=\frac 15\), find \(P(A∩B\)) if A and B are independent events.

A laboratory blood test is \(99\%\) defecting a certain disease when it is, infact present.However the test also yields a falls positive result for \(0.5\%\) of the healthy person tested(i.e.,if a healthy person is tested,then with probability 0.005,the test will imply he has the diesease).If \(0.1\%\) of the population actually has the disease,what is the probability that a person has the disease given that his test result is positive?
In answering a question on a multiple choice test a student either knows the answeror guesses.Let \(\frac{3}{4}\) be the probability that he knows the answer and \(\frac{1}{4}\) be the probability that he guesses.Assuming that the student who guessws the answer,will be correct with probability \(\frac{1}{4}\).What is the probability that a student knows the answer given that he answered it correctly?

Determine (E|F): Mother, Father and son line up at random for a family picture.
E: Son on one end
F: Father in middle

Of the students in a college,it is known that \(60\%\) reside in hostel and \(40\%\) are day scholers.(not residing in hostel).Previous year result report that \(30\%\) of all students who reside in hostel attain A grade and \(20\%\) of day scholars attain A grade in their annual examination.At the end of the year,one student is choosen at random from the college and he has an A grade,What is the probability that the student is a hostler?

Determine P: A coin is tossed three times, where

  1. E: heads on third toss,F:heads on first two tosses.
  2. E: at least two heads,F:at most two heads.
  3. E: at most two tails,F:at least one tail.

\(Evaluate \ P(A∩B)\  if \ 2P(A) = P(B) =\) \(\frac {5}{13}\) \(and \ P(A|B)=\) \(\frac 25\)

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)
A urn contains 5 red and 5 black balls.A ball is drawn at random,its colour is noted and is returned to the urn.Morever,2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random.What is the probability that the second ball is red?

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

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P (E∩F) = 0.2, find P(E|F ) and P(F|E).

In a hostel \(60\%\) of the students read Hindi newspaper,\(40\%\) read English newspaper and \(20\%\) read both Hindi and English newspapers.A student is selected at random.
(a)Find the probability that she reads neither Hindi nor English newspapers.
(b)If she reads Hindi newspaper,find the probability that she reads English newspaper.
(c) If she reads English newspapers,find the probability she reads Hindi newspaper.
Probability of solving specific problem independently by A and B are \(\frac{1}{2}\) and \(\frac{1}{3}\) respectively.If both try to solve the problem independently, find the probability that:
(i)the problem is solved.
(ii)exactly one of them solves the problem.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.Find the probability that:
(i)both balls are red.
(ii)first ball is black and second is red.
(iii)one of them is black and other is red.
A die is tossed thrice. Find the probability of getting an odd number at least once.
Given two independent events \(A\) and \(B\) such that \(P(A)=0.3,P(B)=0.6.\) Find:
(A)\(P(A\, and\, B)\)
(B)\(P(A\, and\, not\, B)\)
(C)\(P(A or B)\)
(D)\(P(neither\, A\, nor\, B)\)
Events \(A\) and \(B\) are such that \(P(A)=\frac{1}{2},P(B)=\frac{7}{12}\) and (not \(A\) or not \(B\))\(=\frac{1}{4}\).State whether \(A\) and \(B\) are independent.
Let A and B independent events, \(P(A)=0.3\) and \(P(B)=0.4\).Find:
(A)\(P(A\cap B)\)
(B)\(P(A\cup B)\)
(C)\(P(A|B)\)
(D)\(P(B|A)\)
Given that the events \(A\) and \(B\) are such that \(P(A)=\frac{1}{2},P(A∪B)=\frac{3}{5}\) and \(P(B)=ρ.\)
Find \(ρ\) if they are(i) mutually exclusive,(ii) independent.
Let E and F be events with \(P(E)=\frac{3}{5},P(F)=\frac{3}{10}\) and \(P(E∩F)=\frac{1}{5}\) .Are E and F independent?