Class 11

Math

JEE Main Questions

Probability I

A coin is tossed three times, consider the following events.A : ‘No head appears’, B: ‘Exactly one head appears’ and C: ‘Atleast two appear’.Do they form a set of mutually exclusive and exhaustive events?

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Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Figure). What is the probability that the fish taken out is a male fish?

A coin is tossed three times, consider the following events. A : ‘No head appears’, B: ‘Exactly one head appears’ and C: ‘Atleast two appear’. Do they form a set of mutually exclusive and exhaustive events?

A and B are two events such that $P(A)=0.54$, $P(B)=0.69$and $P(A∩B)=0.35$.Find (i) $P(A∪B)$ (ii) $P(A_{prime}∩B_{prime})$ (iii) $P(A∩B_{prime})$ (iv) $P(B∩A_{prime})$

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false 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 disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

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

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

Two dice, one blue and one grey, are thrown at the same time. Write down all the possible outcomes. What is the probability that the sum of the two numbers appearing on the top of the dice is(ii) 13?(iii) less than or equal to 12?

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.