Addition and Multiplication Theorems of Probability

IMPORTANT

Addition and Multiplication Theorems of Probability: Overview

This topic covers concepts, such as, Addition Theorem of Probability, Addition Theorem of Probability for Mutually Exclusive Events,B &C etc.

Important Questions on Addition and Multiplication Theorems of Probability

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The probability of solving a problem in Mathematics by two students X and Y are 14 and 15, respectively. If both of them try to solve the problem independently, then the probability that the problem will be solved by exactly one of them is equal to

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M and N are any two events. The probability, that exactly one of them occurs, is

HARD
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For three events, A, B and C, P(Exactly one of A or B occurs)

=P(Exactly one of B or C occurs)

=P(Exactly one of C or A occurs) =14 and P(All the three events occur simultaneously) =116.

Then the probability that at least one of the events occurs, is:

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If AandB are two events such that PAB=PAB, then the incorrect statement amongst the following statements is :

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A and B are two independent events such that PAB=0.8 and PA=0.3. Then, P(B) is

MEDIUM
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A bag contains 5 white and 3 black balls. Two balls are drawn at random without replacement. Determine the probability of getting both the balls black.

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Three faces of a fair die are yellow, two faces red and one blue. The die is thrown twice. The probability that 1st throw will give an yellow face and the second a blue face is

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There are 6 red and 5 black balls in a bag. Two balls are drawn at random one after another with replacement. The probability that both the balls drawn may be red is

HARD
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If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails, is

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Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 34,12 and 58 respectively, then the probability that the target is hit by P or Q but not by R is:

EASY
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A fair dodecahedral die numbered 1, 2, 3, 4, 8, 9, 16, 27, 32, 81, 243 and 729 is thrown and the number noted.

The events C, "thrown an odd number", and D, "throw an event number ", are represented on the venn diagram below:

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Hence show that P(CD)=P(C)+P(D).

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A fair decahedral die numbered 1, 2, 3, ...... 10 is thrown and the number noted.

The events A, 'throw a square number", and B, 'throw a factor of six, are represented on the Venn diagram below:

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Hence show that P(AB)=P(A)+P(B)-P(AB).

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A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then find the least value of n.

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There are 8 laddus, 5 mangoes and 4 samoshas in a sweets box. If 1 Item is picked at random, What is the probability of having either a laddu or a mango ?

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A speaks truth in 75% of the cases and B in 80%, cases. What is the probability that their statements about an incident do not match?

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If P(A)=611, P(B)=511 and P(AB)=711, then value of PAB is 

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There are two bags, bag 1 contains 3 white and 2 red balls and bag 2 contains 4 white and 5 red balls. A ball is drawn randomly from bag 1 and put in bag 2. Now 2 balls are drawn from bag 2 and found to be red. Then the probability that white ball was drawn from bag 1 to bag 2 is
 

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If A, B and C are exhaustive events satisfying PABC¯=15PBC-PABC=115 and PAC=110 then PCAB¯ is equal to

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A fair coin is tossed until one of the 2 sides occurs twice in a row. Probability that even number of tosses required is

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Let P1, P2 and P3 are the probabilities of a student passing three independent exams A, B and C respectively. If P1, P2 and P3 are the roots of equation 20x3-27x2+14x-2=0, then the probability that the student passes in exactly one of A, B and C is