Class 12

Math

Algebra

Probability I

A dice is loaded so that the probability of a face I is proportional to $i_{2}$ , I = 1, 2, …, 6. Then find the probability of occurring a prime number when the dice is rolled.

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A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, III or all the three. The probabilities of the Student passing in tests II and III are m, n and $21 $ respectively. If the probability of the student to be successful is $21 $, then which one of the following is correct? (a) $m(1+n)=1$ (B) $n(1+m)=1$ (C) $m=1$ (D) $mn=1$

A bag contains a total of 20 books on physics and mathematics. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 2 books on mathematics.

Let $AandB$ are events of an experiment and $P(A)=1/4,P(A∪B)=1/2,$ then value of $P(B/A_{c})$ is $2/3$ b. $1/3$ c. $5/6$ d. $1/2$

If the letters of the word REGULATIONS be arranged at random, find the probability that there will be exactly four letters between the $R$ and the$E˙$

For the three events $A,B,andC,P$ (exactly one of the events $AorB$ occurs)$=P$ (exactly one of the two evens $BorC$ )$=P$ (exactly one of the events $CorA$ occurs)$=pandP$ (all the three events occur simultaneously)$=p_{2}whereo<p<1/2.$ Then the probability of at least one of the three events $A,BandC$ occurring is $23p+2p_{2} $ b. $4p+3p_{2} $ c. $2p+3p_{2} $ d. $43p+2p_{2} $

Consider the system of equations ax + by = 0; cx + dy = 0, where $a,b,c,d∈{0,1}$)STATEMENT-1: The probability that the system of equations has a unique solution is 3/8 STATEMENT-2: The probability that the system of equations has a solution is 1

Out of $3n$ consecutive integers, there are selected at random. Find the probability that their sum is divisible by 3.

A dice is thrown six times, it being known that each time a different digit is shown. The probability that a sum of 12 will be obtained in the first three throws is $5/24$ b. $25/216$ c. $3/20$ d. $1/12$