class 12

Math

Algebra

Probability I

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 $

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If the squares of a $8×8$ chessboard are painted either red or black at random. The probability that the chessboard contains equal number of red and black squares is

If two distinct numbers m and n are chosen at random form the set {1, 2, 3, …, 100}, then find the probability that $2_{m}+2_{n}+1$ is divisible by 3.

A car is parked among N cars standing in a row, but not at either end. On his return, the owner finds that exactly 'r' of the N places are still occupied. The probability that the places neighboring his car are empty is

Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is

A shoping mall is running a scheme: Each packet of detergent SURF contains a coupon which bears letter of the word SURF, if a person buys at least four packets of detergent SURF, and produce all the letters of the word SURF, then he gets one free packet of detergent. If person buys 8 such packets, then the probability that he gets exactly one free packets is

Find the probability that a leap year will have 53 Fridays or 53 Saturdays.

Probability if n heads in 2n tosses of a fair coin can be given by

Box 1 contains three cards bearing numbers, 1, 2, 3, box 2 contains five cards bearing number 1, 2, 3, 4, 5, and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_{i}$ be the number on the card drawn from the $i_{th}$ box, i = 1, 2, 3. The probability that $x_{1}+x_{2}+x_{3}$ is odd, is