Class 12

Math

Algebra

Probability I

Fourteen numbered balls (1, 2, 3, …, 14) are divided in 3 groups randomly. Find the probability that the sum of the numbers on the balls, in each group, is odd.

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Suppose you drop a die at random on the rectangular region shown in Figure. What is the probability that it will land inside the circle with diameter 1m?

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing atleast one of them is 0.95. What is the probability of passing both?

A and B are events such that $P(A)=0.42$, $P(B)=0.48$and $P(AandB)=0.16$. Determine (i) P(not A), (ii) P(not B) and (iii) P(A or B)

A coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which first throw is a head, then find $P(E/F)˙$

A rifleman is firing at a distance target and hence has only 10% chance of hitting it. Find the number of rounds; he must fire in order to have more than 50% chance of hitting it at least once.

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that(a) you both enter the same section?(b) you both enter the different sections?

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1,2,3,4,5,6,1,8 (see Figure), and these are equally likely outcomes. What is the probability that it will point at(i) 8?(ii) an odd number?(iii) a number greater than 2?(iv) a number less than 9?

A die is rolled thrice, find the probability of getting a larger number each time than the previous number.