Binomial Distribution (Edexcel A-Level Mathematics): Quizzes

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The Binomial Distribution
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How many possible outcomes does each trial have in a binomial distribution?

Two outcomes

In the notation X∼B(n,p)X \sim B(n, p), what does nn represent?

Number of trials

In the notation X∼B(n,p)X \sim B(n, p), what does pp represent?

Probability of success each time

In X∼B(n,p)X \sim B(n, p), what does the random variable XX represent?

Number of wins obtained

Which assumption is required for a binomial distribution?

Trials are independent

What is the formula for P(X=x)P(X = x) in a binomial distribution?

(nx)px(1−p)n−x\binom{n}{x} p^x (1-p)^{n-x}

If X∼B(n,p)X \sim B(n, p), what is the mean of XX?

npnp

If X∼B(n,p)X \sim B(n, p), what is the variance of XX?

np(1−p)np(1-p)

How is P(X≤1)P(X \leq 1) calculated?

P(X=0)+P(X=1)P(X = 0) + P(X = 1)

Which scenario is suitable for binomial distribution modeling?

10 switches, each faulty with prob 0.08

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