class 12

Math

Algebra

Probability I

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

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In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that(i) The student opted for NCC or NSS.(ii) The student has opted neither NCC nor NSS.(iii) The student has opted NSS but not NCC.

The probability that certain electronic component fail, when first used is 0.10. If it does not fail immediately, then the probability that it lasts for one year is 0.99. What is the probability that a new component will last for one year?

Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.

How many times must a man toss a fair com so that the probability of having at least one head is more than 90%?

If two events $AandB$ are such that $P(A_{c})=0.3,P(B)=0.4,andP(A∩B_{c})=0.5$ , then find the value of $P[B/(A∪B_{c})]˙$

A fair coin is tossed $n$ times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value of $n˙$

Complete the following statements : (i) Probability of an event E + Probability of the event 'not E' = _____________ .(ii) The probability of an event that cannot happen is________ Such an event is called __________ .(iii) The probability of an event that is certain to happen is ______. Such an event is called __________ .(iv) The sum of the probabilities of all the elementary events of an experiment is __________ .(v) The probability of an event is greater than or equal to ________ and less than or equal to _________ .

A mapping is select at random from the set of all the mappings of the set $A={1,2,n}$ into itself. Find the probability that the mapping selected is an injection.