Probability — Class 12 solved problems

16 problems from this chapter, each solved step by step.

(a) Two cards are drawn at random and one by one with replacement from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number
(i) The probability of no defective screws is approximately 0.1353. (ii) The probability of one defective screw is approximately 0.2706.
If the probability that the random variable X takes the value x is given by P(X=x)=k (x+1)3^(-x), x=0,1,2,, where k is a constant, then P(X 3) is equal to:
(1)/(9)
A fair coin is flipped repeatedly. What is the expected number of flips until the pattern HTH appears?
The expected number of flips until the pattern HTH appears is 10.
A candidate has to reach the examination center in time. The probability that he travels by metro, bus, or taxi are 3/10, 1/5, and 1/10 respectively, and 2/5 by
The probability that he travelled by metro, given that he reached the center in time, is (32)/(107).
A bag contains 19 unbiased coins and one coin with heads on both sides. One coin drawn at random is tossed and a head turns up. If the probability that the draw
80
Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag
6
Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are dr
The variance of x is (28)/(75).
Let a random variable X take values 0, 1, 2 and 3 with P(X = 0) = P(X = 1) = p and P(X = 2) = P(X = 3) = (1 - 2p)/(2). If E(X²) = 2E(X), then the value of 8p -
0
Two players take turns rolling a fair die. Player A wins if he rolls a 6, Player B wins if he rolls a 5 or 6. If A starts, find the probability that A wins.
The probability that A wins is (3)/(8).
A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is:
The variance of X is (28)/(75).
Given three identical bags each containing 10 balls, whose colours are as follows: Bag I: Red = 3, Blue = 2, Green = 5 Bag II: Red = 4, Blue = 3, Green = 3 Bag
7
Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball
14
A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card being a s
n = 2
If A and B are two events such that P(A B)=0.1, and P(A B) and P(B A) are the roots of the equation 12x²-7x+1=0, then the value of P( A B)P( A B) is:
2.25
A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of
The probability that A wins is (9)/(19).
A coin is tossed three times. Let X denote the number of times a tail follows a head. If and ² denote the mean and variance of X, then the value of 64( + ²) is:
48

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