#binomial distribution

General Mathematics 4

P [X = x] = nCx px qn-x is the formula for _____

Let's break it down: solving fully: apply relevant formula, put numbers, compute. Result comes as binomial distribution. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI and XII

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Probability 2

The mean and the variance in a binomial distribution are found to be 2 and 1 respectively. The probability P(X = 0) is

We know that using formula we get 1/16. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 1/16.

Ref: NCERT Mathematics Class XII — Probability

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Probability 2

In an examination, the probability of a candidate solving a question is 1/2. out of given 5 questions in the examination

Think of it like this: we verify 13/16 by full calculation: use standard identity, substitute, simplify step by step to reach 13/16.

Ref: NCERT Mathematics Class XII — Probability

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Probability 2

Let the random variables X follow B (6, p) If 16;P;( X = 4 ) = P;( X = 2 ) , then what is the value of p

Look at it this way: solving fully: apply relevant formula, put numbers, compute. Result comes as 1/5. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XII — Probability

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Probability 2

Which among the following is the standard deviation of Binomial distribution?

The trick is using formula we get npq. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get npq.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

In a binomial distribution, the mean is 4 and variance is 3. Then the mode is

In easy words, np=4, npq=3 gives q=0.75,p=0.25,n=16. Mode=floor((n+1)p)=floor(4.25)=4. Complete.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

Out of 800 families with 4 children each, how many families would be expected to have 2 boys and 2 girls.

We can see that complete solution: write formula, plug data, do arithmetic. Final value matches 300. Simple and accurate.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

Let variable X has a binomial distribution B(6, 12) . Then the most likely outcome is when the value of X is _______.

Applying the basic concept, we verify 3 by full calculation: use standard identity, substitute, simplify step by step to reach 3.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

The binomial distribution has

In easy words, binomial needs fixed n, independent trials, P=nCr p^r q^(n-r), mean=np, variance=npq, mode floor((n+1)p). Complete properties.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes?

Look at it this way: after simplifying, 25216 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

The mean and variance of a binomial distribution are 8 and 4 respectively, then p(x = 1) is equal to-

Look at it this way: np=8, npq=4 gives q=0.5, p=0.5, n=16. Then P(X=1)=16C1(0.5)^16=16/65536=1/4096. Complete.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

If the mean and the variance of a binomial variate Y are 2 and 1 respectively, then the probability that Y takes a value

We know that np=2, npq=1, so q=0.5, p=0.5, n=4. P(Y≥1)=1-P₀=1-(0.5)⁴=1-1/16=15/16. Full binomial calculation.

Ref: NCERT Mathematics Class XII — Probability

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