Class 12

Math

Algebra

Probability I

Three randomly chosen non-negative integers x, y and z are found to satisfy the equation x + y + z 10. Then the probability that z is even, is

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A fair coin is tossed repeatedly. If tail appears on first four tosses, then find the probability of head appearing on fifth toss.

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?

4 cards are drawn from a well - shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

Five cards—the ten, jack, queen, king and ace of diamonds, are well shuffled with their face downwards. One card is then picked up at random.(i) What is the probability that the card is the queen?(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

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 $n˙$

One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will(i) be an ace.(ii) not be an ace.

Probability that A speaks truth is $54 $ . A coin is tossed. A reports that a head appears. The probability that actually there was head is (A) $54 $ (B)$21 $ (C) $51 $ (D) $52 $

Describe the sample space for the indicated experiment : A coin is tossed four times.