class 12

Math

Algebra

Probability I

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is :

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The probability that a student will pass the final examination m both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability' of passing the Hindi examination?

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

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 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?

Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A coins is flipped once. If it shows a head, the game continues by throwing die A: if it shows tail, then die B is to be used. If the probability that die A is used is 32/33 when it is given that red turns up every time in first $n$ throws, then find the value of $n˙$

A coin is tossed and a dice is rolled. Find the probability that the coin shows the head and the dice shows 6.

Describe the sample space for the indicated experiment : 2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

A die is thrown twice. What is the probability that(i) 5 will not come up either time? (ii) 5 will come up at least once?[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]