Class 12

Math

Algebra

Probability I

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

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An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A coins is flipped once. If it shows a head, the game continues by throwing die A: if it shows tail, then die B is to be used. If the probability that die A is used is 32/33 when it is given that red turns up every time in first $n$ throws, then find the value of $n˙$

A bag contains $W$ white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. Then find the probability that this procedure for drawing the balls will come to an end at the rth draw.

$AandB$ play a series of games which cannot be drawn and $p,q$ are their respective chance of winning a single game. What is the chance that $A$ wins $m$ games before $B$ wins $n$ games?

How many times must a man toss a fair com so that the probability of having at least one head is more than 90%?

If four whole numbers taken at random are multiplied together, then find the probability that the last digit in the product is 1,3,7 or 9.

Describe the sample space for the indicated experiment : One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

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 ?