Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board chapter 8 - Binomial Distribution [Latest edition]

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of 5 successes. 

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at least 5 successes.

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at most 5 successes.

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

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards; find the probability that all the five cards are spades.

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that only 3 cards are spades

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards; find the probability that none is a spade.

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one, will fuse after 150 days of use.

A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is ${\displaystyle \frac{1}{100}}$. What is the probability that he will win a prize at least once. 

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $$\frac{1}{100}.$$  What is the probability that he will win a prize exactly once.

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $$\frac{1}{100}.$$  What is the probability that he will win a prize at least twice.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that none of the floppy disc work.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly one floppy disc work.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly two floppy disc work.

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that all 3 of the sample will work.

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

Given X ~ B(n, P) if n = 10 and p = 0.4, find E(x) and Var(X).

Given X ~ B(n, p) if p = 0.6 and E(X) = 6, find n and Var(X).

Given X ~ B(n, P) if n = 25 and E(X) = 10, find p and SD(X).

Given X ~ B(n, P) if n = 10, E(X) = 8, find Var(X).

Choose the correct option from the given alternatives:

A die is thrown 100 times. If getting an even number is considered a success, then the standard deviation of the number of successes is ______.

Choose the correct option from the given alternatives:

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

Choose the correct option from the given alternatives:

For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______

Choose the correct option from the given alternatives:

For a binomial distribution, n = 4. If 2P(X = 3) = 3P(X = 2), then p = ______

If X ~ B(4, p) and P(X = 0) = ${\displaystyle \frac{16}{81}}$, then P(X = 4) = ______.

Choose the correct option from the given alternatives:

The probability of a shooter hitting a target is ${\displaystyle \frac{3}{4}}$ How many minimum numbers of times must he fire so that the probability of hitting the target at least once is more than 0·99?

If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.

Let X ~ B(10, 0.2). Find P(X = 1).

Let X ~ B(10, 0.2). Find P(X ≥ 1).

Let X ~ B(10, 0.2). Find P(X ≤ 8).

Let X ~ B(n, p) if n = 10, E(X) = 5, find p and Var(X).

Let X ~ B(n, p) if E(X) = 5 and Var(X) = 2.5, find n and p.

If a fair coin is tossed 10 times and the probability that it shows heads 5 times.

If a fair coin is tossed 10 times and the probability that it shows heads in the first four tosses and tail in last six tosses.

The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 2 will miss the target.

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: exactly one has a burst tyre

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: at most three have a burst tyre

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: two or more have burst tyre.

The probability that a lamp in a classroom will be burnt out is 0.3. Six such lamps are fitted in the class-room. If it is known that the classroom is unusable if the number of lamps burning in it is less than four, find the probability that the classroom cannot be used on a random occasion.

A lot of 100 items contain 10 defective items. Five items are selected at random from the lot and sent to the retail store. What is the probability that the store will receive at most one defective item?

A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. The inspector of the retailer picks 20 items from a shipment. What is the probability that the store will receive at most one defective item?

The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly two of the next four components tested will survive.

An examination consists of 10 multiple choice questions, in each of which a candidate has to deduce which one of five suggested answers is correct. A completely unprepared student guesses each answer completely randomly. What is the probability that this student gets 8 or more questions correct? Draw the appropriate morals.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that all 8 machines.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that 7 or 8 machines.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that at most 6 machines will produce all bolts within specification. 

The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, calculate the probability that 38 or more will not develop any faults within the first 3 years of use.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 0.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 1.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 2.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 3 or more, terminals will require attention during the next week.

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Calculate the probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of the pupils.

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.

Find the probability that the visitor obtains answer yes from at least 2 pupils:

1. when the number of pupils questioned remains at 4.
2. when the number of pupils questioned is increased to 8.

It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.

It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of given week.

If the probability of success in a single trial is 0.01. How many trials are required in order to have a probability greater than 0.5 of getting at least one success?

In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.