A coin is tossed 6 times. Find the probability of getting at least 3 heads.

A coin is tossed 5 times. What is the probability that a head appears an even number of times?

7 coins are tossed simultaneously. What is the probability that a tail appears an odd number of times?

A coin is tossed 6 times. Find the probability of getting

(i) exactly 4 heads

(ii) at least 1 heads

(iii) at most 4 heads

10 coins are tossed simultaneously. Find the probability of getting

(i) exactly 3 heads

(ii) not more than 4 heads

(iii) at least 4 heads

A die is thrown 6 times. If ‘getting an even number’ is a success, find the probability of getting

(i) exactly 5 successes

(ii) at least 5 successes

(iii) at most 5 successes

A die is thrown 4 times. ‘Getting a 1 or a 6’ is considered a success, Find the probability of getting

(i) exactly 3 successes

(ii) at least 2 successes

(iii) at most 2 successes

Find the probability of a 4 turning up at least once in two tosses of a fair die.

A pair of dice is thrown 4 times. If ‘getting a doublet’ is considered a success, find the probability of getting 2 successes.

A pair of dice is thrown 7 times. If ‘getting a total of 7’ is considered a success, find the probability of getting

(i) no success

(ii) exactly 6 successes

(iii) at least 6 successes

(iv) at most 6 successes

There are 6% defective items in a large bulk of times. Find the probability that a sample of 8 items will include not more than one detective item.

In a box containing 60 bulbs, 6 are defective. What is the probability that out of a sample of 5 bulbs

(i) none is defective

(ii) exactly 2 are defective

The probability that a bulb produced by a factory will fuse after 6 months of use is 0.05. find the probability that out of 5 such bulbs

(i) none will fuse after 6 months of use

(ii) at least one will fuse after 6 months of use

(iii) not more than one will fuse after 6 months of use

In the items produced by a factory, there are 10% defective items. A sample of 6 items is randomly chosen. Find the probability that this sample contains.

(i) exactly 2 defective items

(ii) not more than 2 defective items

(iii) at least 3 defective items

Assume that on an average one telephone number out of 15, called between 3 p.m. on weekdays, will be busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?

Three cars participate in a race. The probability that any one of them has an accident is 0.1. Find the probability that all the cars reach the finishing line without any accident.

Past records show that 80% of the operations performed by a certain doctor were successful. If the doctor performs 4 operations in a day, what is the probability that at least 3 operations will be successful?

The probability of a man hitting a target is (1/4). If he fires 7 times, what is the probability of his hitting the target at least twice?

In a hurdles race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is (5/6). What is the probability that he will knock down fewer than 2 hurdles?

A man can hit a bird, once in 3 shots. On this assumption he fires 3 shots. What is the chance that at least one bird is hit?

If the probability that a man aged 60 will live to be 70 is 0.65, what is the probability that out of 10 men, now 60, at least 8 will live to be 70?

A bag contains 5 white, 7 red 8 black balls. If four balls are drawn one by one with replacement, what is the probability that

(i) None is white

(ii) All are white

(iii) At least one is white

A policeman fires 6 bullets at a burglar. The probability that the burglar will be hit by a bullet is 0.6. what is the probability that burglar is still unhurt?

A die is tossed thrice. A success is 1 or 6 on a toss. Find the mean and variance of successes.

A die is thrown 100 times. Getting an even number is considered a success. Find the mean and variance of success.

Determine the binomial distribution whose mean is 9 and variance is 6?

Find the binomial distribution whose mean is 5 and variance is 2.5.

The mean and variance of a binomial distribution are 4 and (4/3) respectively. Find P(X≥ 1).

For a binomial distribution, the mean is 6 and the standard deviation is . Find the probability of getting 5 successes.

In a binomial distribution, the sum and the product of the mean and the variance are (25/3) and (50/3) respectively. Find the distribution.

Obtain the binomial distribution whose mean is 10 and standard deviation is .

Bring out the fallacy, if any, in the following statement:

‘The mean of a binomial distribution is 6 and its variance is 9’

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If A and B are mutually exclusive events such that P(A) = 0.4, P(B) =x and P(A ∪ B) = 0.5, then x = ?

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If A and B are independent events such that P(A) = 0.4, P(B) = x and P(A ∪ B) = 0.5, then x = ?

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If P(A) = 0.8, P(B) = 0.5 and P(B/A) = 0.4, then P(A/B) =?

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If P(A) = , P(B) = and P(A ∪ B) = , then P(A/B)=?

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If A and B are events such that P(A) = , P(B) = and P(A’ ∪ B’) = , then A and B are

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It is given that the probability that A can solve a given problem is and the probability that B can solve the same problem is . The probability that at least one of A and B can solve a problem is

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The probabilities of A, B and C of solving a problem are , and respectively. What is the probability that the problem is solved?

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A can hit a target 4 times in 5 shots, B can hot 3 times in 4 shots, and C can hit 2 times in 3 shots. The probability that B and C hit and A does not hit is

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A machine operates only when all of its three components function. The probabilities of the failures of the first, second and third component are 0.2, 0.3 and 0.5, respectively. What is the probability that the machine will fail?

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A die is rolled. If the outcome is an odd number, what is the probability that it is prime?

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If A and B are events such that P(A) = 0.3, P(B) = 0.2 and P(A ∩ B) = 0.1, then P(∩ B) = ?

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If P(A) = , P(B) = and P(A ∩ B) = , then P(= ?

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If A and B are events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then P(A/B) =?

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If A and B are independent events, then P=?

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If A and B are two events such that P(A ∪ B) = , P(A ∩ B) = and P() = , then the events A and B are

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A die is thrown twice, and the sum of the numbers appearing is observed to be 7. What is the conditional probability that the number 2 has appeared at least one?

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In a class, 60% of the students read mathematics, 25% biology and 15% both mathematics and biology. One student is selected at random. What is the probability that he reads mathematics if it is known that he reads biology?

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A couple has 2 children. What is the probability that both are boys. If it is known that one of them is a boy?

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An unbiased die is tossed twice. What is the probability of getting a 4, 5 or 6 on the first toss and a 1, 2, 3 or 4 on the second toss?

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A fair coin is tossed 6 times. What is the probability of getting at least 3 heads?

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A coin is tossed 5 times. What is the probability that tail appears an odd number of times?

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A coin is tossed 5 times. What is the probability that the head appears an even number of times?

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8 coins are tossed simultaneously. The probability of getting at least 6 heads is

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A die is thrown 5 times. If getting an odd number is a success, then what is the probability of getting at least 4 successes?

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In 4 throws of a pair of dice, what is the probability of throwing doublets at least twice?

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A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, what is the probability of getting at most 6 successes?

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The probability that a man can hit a target is . He tries five times. What is the probability that he will hit the target at least 3 times?

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The probability of the safe arrival of one ship out of 5 is . What is the probability of the safe arrival of at least 3 ships?

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The probability that an event E occurs in one trial is 0.4, Three independent trials of the experiment are performed. What is the probability that E occurs at least once?