class 12

Math

Algebra

Probability

Three randomly chosen nonnegative integers $x,yandz$are found to satisfy the equation $x+y+z=10.$Then the probability that $z$is even, is:$125 $ (b) $21 $ (c) $116 $ (d) $5536 $

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An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver.

If C and D are two events such that $C⊂DandP(D)=0$, then the correct statement among the following is :

There are five students $S_{1},S_{2},S_{3},S_{4}$and $S_{5}$in a music class and for them there are five seats $R_{1},R_{2},R_{3},R_{4}$and $R_{5}$arranged in a row, where initially the seat $R_{i}$is allotted to the student $S_{i},i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted five seats.The probability that, on the examination day, the student $S_{1}$gets the previously allotted seat $R_{1}$, and NONE of the remaining students gets the seat previously allotted to him/her is$403 $(b) $81 $(c) $407 $(d) $51 $

Let $A$ and $B$ be the events such that $P(A)=115 ,P(B)=116 $ and $P(A∪B)=117 $.Find $P(B/A)$

In a hostel $60%$ of the students read Hindi newspaper, $40%$ read English newspaper and $20%$ read Hindi and English newspapers. A student is selected at random.Find the probability that he reads neither Hindi nor English newspaper.

Let $A$ and $B$ be the events such that $P(A)=103 ,P(B)=21 $ and $P(B/A)=52 $.Find $P(A/B)$

Four cards are drawn successively with replacement from a well shuffled deck of 52 cards. What is the probability that (i) all the four cards are spades ?(ii) only 2 cards are spades ?

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is