Class 12

Math

Algebra

Probability I

Two natural numbers x and y are chosen at random. What is the probability that $x_{2}+y_{2}$ is divisible by 5?

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

A fair coin is tossed $n$ times. if the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then find the value of $n˙$

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

$AandB$ are two candidates seeking admission in ITT. The probability that $A$ is selected is 0.5 and the probability that $AandB$ are selected is at most 0.3. Is it possible that the probability of $B$ getting selected is 0.9?

A, B, C in order draws a card from a pack of cards, replacing them after each draw, on condition that the first who draws a spade shall win a prize : find their respective chances.

The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

A bag contains 9 discs of which 4 are red. 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag.Calculate the probability that it will be (i) red. (ii) yellow, (iii) blue, (iv) not blue,(v) either red or yellow.