Class 12

Math

Algebra

Probability I

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

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If $AandB$ are two independent events such that $P(A)=1/2andP(B)=1/5,$ then a.$P(A∪B)=3/5$ b. $P(A/B)=1/4$ c. $P(A/A∪B)=5/6$ d. $P(A∩B/A∪B)=0$

Two numbers are selected randomly from the set $S={1,2,3,4,5,6}$ without replacement one by one. The probability that minimum of the two numbers is less than 4 is (a) $151 $ (b) $1514 $ (c) $51 $ (d) $54 $

A bag contains 20 coins. If the probability that the bag contains exactly 4 biased coin is 1/3 and that of exactly 5 biased coin is 2/3, then the probability that all the biased coin are sorted out from bag is exactly 10 draws is

Mr. A lives at origin on the Cartesian plane and has his office at $(4,5)$ His friend lives at $(2,3)$ on the same plane. Mrs. A can go to his office travelling one block at a time either in the $+yor+x$ direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considere (a) $21 $ (b) $2110 $ (c) $41 $ (d) $2111 $

An unbiased die is such that probability of number $n$ appearing is proportional to $n_{2}(n=1,2,3,4,5,6)˙$ The die is rolled twice, giving the numbers $aandb$ . Then find the probability that $a<b˙$

A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that the sum of two numbers thrown is even is $1/12$ b. $1/6$ c. $1/3$ d. $5/9$

A bag contains a total of 20 books on physics and mathematics. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 2 books on mathematics.

A fair die is thrown 20 times. The probability that on the 10th throw, the fourth six appears is a.$_{20}C_{10}×5_{6}/6_{20}$ b. $120×5_{7}/6_{10}$ c. $84×5_{6}/6_{10}$ d. none of these