Class 12

Math

Algebra

Probability I

A five-digit number is formed by the digit 1, 2, 3, 4, 5 without repetition. Find the probability that the number formed is divisible by 4.

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(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?

A card is selected from a pack of 52 cards.(a) How many points are there in the sample space?(b) Calculate the probability that the card is an ace of spades.(c) Calculate the probability' that the card is (i) an ace (ii) black card.

Describe the sample space for the indicated experiment : A die is thrown two times.

If $P(A∪B)=3/4andP(A)=2/3$ , then find the value of $P(A∩B)˙$

Describe the sample space for the indicated experiment : A coin is tossed and a die is thrown.

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 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 ?

A rifleman is firing at a distance target and hence has only 10% chance of hitting it. Find the number of rounds; he must fire in order to have more than 50% chance of hitting it at least once.