Class 12

Math

Algebra

Probability I

Two integers x and y are chosen with replacement out of the set {0, 1, 2, 3, …, 10}. Then find the probability that $∣x−y∣>5$.

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On a Saturday night, 20%of all drivers in U.S.A. are under the influence of alcohol. The probability that a drive under the influence of alcohol will have an accident is 0.001. The probability that a sober drive will have an accident is 0.0001. if a car on a Saturday night smashed into a tree, the probability that the driver was under the influence of alcohol is $3/7$ b. $4/7$ c. $5/7$ d. $6/7$

If $AandB$ each toss three coins. The probability that both get the same number of heads is (a) $91 $ (b) $163 $ (c) $165 $ (d) $83 $

A fair coin is tossed 100 times. The probability of getting tails 1, 3, .., 49 times is $1/2$ b. $1/4$ c. $1/8$ d. $1/16$

Let $A,B,C$ be three events such that \displaystyle{P}{\left({A}\right)}={0}.{3},{P}{\left({B}\right)}={0}.{4},{P}{\left({C}\right)}={0}.{8},{P}{\left({A}\cap{B}\right)}={0}.{88},{P}{\left({A}\cap{C}\right)}={0}.{28},{P}{\left({A}\cap{B}\cap{C}\right)}={0}.{09}. If $P(A∪B∪C)≥0.75,$ then show that $0.23≤P(B∩C)≤0.48.$

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

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 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.

Three houses are available in a locality. Three persons apply for the houses. Each applies for one houses without consulting others. The probability that all three apply for the same houses is $1/9$ b. $2/9$ c. $7/9$ d. $8/9$