Class 12

Math

Algebra

Probability

If $A$ and $B$ are two events such that $P(A)=0.3$, $P(B)=0.25$, $P(A∩B)=0.2$, then $P((B_{C}A_{C} )_{C})$ is equal to

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Probability of solving specific problem independently by A and B are $21 $and $31 $respectively. If both try to solve the problem independently, find the probability that(i) the problem is solved(ii) exactly one of them solves the problem.

A random variable X has the following probability distribution: $I$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $P(X)$ $0$ $K$ $2K$ $2K$ $3K$ $K_{2}$ $2K_{2}$ $7K_{2}+K$Determine:(i) K (ii) P(X<3) (iii) P(X > 6) (iv) P (0 < X < 3)

A coin is tossed if head turns up then pair of dice is thrown and sum of numbers is noted. If tail turns up then a card numbered from 1 to 9 is drawn and number is noted, then find the probability that number is $7or8$. (a) $3613 $ (b) $7215 $ (c) $7219 $ (d) $3611 $

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $53 $be the probability that he knows the answer and $52 $be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $31 $, what is the probability that the student knows the answer given that he answered it correctly

Two unbaised dice are thrown. Find the probability that the sum of the numbers appearing is $8$ or greater, if $4$ appear on the first head.

A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that it is neither a king nor a heart.