A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of success.

12 cards, numbered 1 to 12, are placed in box mixed up thoroughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number.

In a bulb factory machines A, B and C manufacture 60%, 30% and 10% bulbs respectively. 1%, 2% and 3% of the bulbs produced respectively by A, B and C are found to be defective. Find the probability that this bulb was produced by the machine A.

The probabilities of A, B, C solving a problem are \(\frac { 1 }{ 3 } ,\frac { 2 }{ 7 } and\frac { 3 }{ 8 } \) respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them can solve it.

A die is throewn again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

A pair of dice is thrown 4 times. If getting a doublet is considered a success find the mean and variance of the number of successes.

From a lot of 30 bulbs which includes 6 defectives, a samole of 4 bulbs is drawn at random with replacement. Find the mean and variance of the number of defective bulbs.

Probabilities of solving a specific problem independently by A and B are \(1\over2\) and \(1\over3\) respectively. If both try to solve the problem independently, find the probability that
(i) the problem is solved
(ii) exactly one of them solves the problem.

Given three identical boxes I, II and III, each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in the box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?

A husband and a wife appear in an interview for two vacancies for the same post. The probability of husbands selection is \(1\over7\) and that of wife's selection is \(1\over5\). What is the probability that
(i) both will be selected
(ii) only one of them will be selected  
(iii) none will be selected?

An insurance company insured 2,000 cyclists, 4,000 scooter drivers and 6,000 motorbike drivers. The probability of an accident involving a cyclist, scooter driver and a motorbike driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?
Which mode of transport would you suggest to a student and why?

A man is known to speak the truth 3 out of 5 times. He throws a die and reports that it is 1. Find the probability that it is actually 1.

A card from a pack of 52 playing cards is lost. From the remaining cards of the pack, three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.

An urn contains 4 balls. Two balls are drawn at random from the urn (without replacement) and are found to be white, What is the probability that all the four balls in the urn are white?

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and two balls are drawn at random (without replacement) from the bag which are both found to be red. Find the probability that the balls are drawn from the first bag.

Find the mean, the variance and the standard deviation of the number of doublets in three throws of a pair of dice.

An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also, find mean and variance of distribution.

Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence, find the mean and variance of the distribution.

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards at random and are found to be hearts. Find the probability of the missing card to be a heart

Two numbers are selected at random (without replacement) from the first six positive integers.Let x denote the larger of the two numbers obtained.Find the probability distribution of random variable x and hence find the mean of the distribution.