Class 12

Math

Algebra

Probability I

A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of any two consective digits of the number is prime is

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There are two urns $AandB$ . Urn $A$ contains 5 red, 3 blue and 2 white balls, urn $B$ contains 4 red, 3 blue, and 3 white balls. An urn is chosen at random and a ball is drawn. Probability that ball drawn is red is a.$9/10$ b. $1/2$ c. $11/20$ d. $9/20$

If $n$ persons are seated on a round table, what is the probability that two named individuals will be neighbours?

Consider $f(x)=x_{3}+ax_{2}+bx+c$ Parameters $a,b,c$ are chosen as the face value of a fair dice by throwing it three times Then the probability that $f(x)$ is an invertible function is (A) $365 $ (B) $368 $ (C) $94 $ (D) $31 $

A fair die is tossed repeatedly. $A$ wins if if is 1 or 2 on two consecutive tosses and $B$ wins if it is 3,4,5 or 6 on two consecutive tosses. The probability that $A$ wins if the die is tossed indefinitely is $1/3$ b. $5/21$ c. $1/4$ d. $2/5$

The probability that at least one of the events $AandB$ occurs is 0.6. If $AandB$ occur simultaneously with probability 0.2, then find $P(A)+P(B)˙$

Four person independently solve a certain problem correctly with probabilities $21 ,43 ,41 ,81 ˙$ Then the probability that he problem is solve correctly by at least one of them is $256235 $ b. $25621 $ c. $2563 $ d. $256253 $

Two integers are chosen at random and multiplied. Find the probability that the product is an even integer.

A card is drawn from an ordinary pack of 52 cards and a gambler bets that, it is a spade or an ace. What are the odds against his wining this bet?