###### Advertisements

###### Advertisements

**Fill in the blank :**

In Binomial distribution probability of success **Remains constant / independent** from trial to trial.

###### Advertisements

#### Solution

In Binomial distribution probability of success _______ from trial to trial.

#### APPEARS IN

#### RELATED QUESTIONS

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

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.

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.

**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:**

The probability of a shooter hitting a target is `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?

**Choose the correct option from the given alternatives:**

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).

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: two or more have burst tyre.

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 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.

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:

- when the number of pupils questioned remains at 4.
- 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.

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.

If E(x) > Var(x) then X follows _______.

In Binomial distribution if n is very large and probability success of p is very small such that np = m (constant) then _______ distribution is applied.

**Solve the following problem :**

An examination consists of 5 multiple choice questions, in each of which the candidate has to decide which one of 4 suggested answers is correct. A completely unprepared student guesses each answer completely randomly. Find the probability that,

- the student gets 4 or more correct answers.
- the student gets less than 4 correct answers.

**Choose the correct alternative:**

A sequence of dichotomous experiments is called a sequence of Bernoulli trials if it satisfies ______

In Binomial distribution, probability of success ______ from trial to trial

**State whether the following statement is True or False:**

For the Binomial distribution, Mean E(X) = m and Variance = Var(X) = m

If the sum of the mean and the variance of a binomial distribution for 5 trials Is 1.8, then p = ______.

If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______

In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.

In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.

If X∼B (n, p) with n = 10, p = 0.4 then E(X^{2}) = ______.

In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = ______.

A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of getting at least two success.

Solution:

A pair of dice is thrown 3 times.

∴ n = 3

Let x = number of success (doublets)

p = probability of success (doublets)

∴ p = `square`, q = `square`

∴ x ∼ B (n, p)

P(x) = ^{n}C_{x}p^{x} q^{n–x}

Probability of getting at least two success means x ≥ 2.

∴ P(x ≥ 2) = P(x = 2) + P(x = 3)

= `square` + `square`

= `2/27`