Class 12

Math

Algebra

Probability I

Four fair dices are thrown simultaneously. Find the probability that the highest number obtained is 4.

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Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experimentA: ‘the sum is even’.B: ‘the sum is a multiple of 3’.C: ‘the sum is less than 4’.D: ‘the sum is greater than 11’.Which pairs of these events are mutually exclusive?

Probability that A speaks truth is $54 $ . A coin is tossed. A reports that a head appears. The probability that actually there was head is (A) $54 $ (B)$21 $ (C) $51 $ (D) $52 $

A pack of playing cards was found to contain only 51 cards. If the first 13 cards, which are examined are all red, then the probability that the missing card is black is :-

Describe the sample space for the indicated experiment : A coin is tossed three times.

A carton consists of 100 shirts of which 88 are good. 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that(i) it is acceptable to Jimmy?(ii) it is acceptable to Sujatha?

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

A die is thrown. Describe the following events:(i) A : a number less than 7 (ii) B : a number greater than 7(iii) C : a multiple of 3 (iv) D : a number less than 4(v) E : a even number greater than 4(vi) F : a number not less than 3 Also find \displaystyle{A}

A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that(i) She will buy it?(ii) She will not buy it ?