Binomial Distribution

IMPORTANT

Binomial Distribution: Overview

This topic covers concepts such as Bernoulli Trials, Binomial Probability Distribution, Mean in Binomial Probability Distribution, Variance in Binomial Probability Distribution, and Standard Deviation in Binomial Probability Distribution.

Important Questions on Binomial Distribution

MEDIUM
IMPORTANT

One hundred identical coins, each with probability p of showing up heads are tossed once. If 0<p<1 and the probability of heads showing on 50 coins is equal to the probability of heads showing on 51 coins, then value of p is:

MEDIUM
IMPORTANT

Fifteen coupons are numbered 1, 2, 3,..., 15, respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is:

EASY
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The probability that an event A happens in one trial of an experiment is 0.4 . Three independent trials of the experiment are performed. The probability that the event A happens at least once is

EASY
IMPORTANT

Find the expectation of number of heads in 30 tosses of a fair coin.

EASY
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The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university all will graduate.

EASY
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The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university only one will graduate.

EASY
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A coin is tossed 999 times. If X is the number of times heads appeared, then P(X=r) if maximum when r=

HARD
IMPORTANT

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least 0.96, is

EASY
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In five throws with a pair of dice, what is the probability of throwing doublets at least thrice?

EASY
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An unbiased coin is tossed 6 times. Find, using binomial distribution, the probability of getting at least 5 heads.

EASY
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Suppose X follows a binomial distribution with parameters n=6 and p. If 16P(X=4)=P(X=2), then 8p is equal to

MEDIUM
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The probability of hitting a target in any shot is 0.2. If 10 shots are fired, find the probability that the target will be hit at least twice.

EASY
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Given that X~Bn=10,p. If E(X)=8 find the value of p.

MEDIUM
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It is possible for a computer to pick up an erroneous signal that does not show up as an error on the screen. The error is called a silent error. A particular terminal is defective and when while using the system "word processor" it introduces a silent paging error with probability 0.1. The word processor is used 20 times during a given week.Then the probability that no silent paging errors occus is 

MEDIUM
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A radar complex consists of eight units that operate independently. The probability that a unit detects an incoming missile is 0.9.If the probability that an incoming missile will not be detected by any unit is a-8, then find a.

EASY
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If EX=5 and  VarX=2.5, find n+p.

MEDIUM
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A fair coin is tossed 9 times. Find the probability that it shows heads exactly 5 times.

EASY
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Let X~Bn, p, If n=10, EX=5, then find p.

HARD
IMPORTANT

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least 0.96, is

EASY
IMPORTANT

A fair coin is tossed 9 times. The probability that it shows head exactly 5 times is