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Binomial & Poisson Distributions · Question 14 of 68

Question 14

MediumOriginal question

XX follows a binomial distribution with n=7n = 7 and p=0.4p = 0.4. Which expression is P(X=3)P(X = 3)?

Options for question 14

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. P(X=r)=nCr prqn−rP(X = r) = {}^{n}C_{r}\,p^{r}q^{n - r}, with q=1−p=0.6q = 1 - p = 0.6.

  2. For r=3r = 3: 7C3 (0.4)3(0.6)4{}^{7}C_{3}\,(0.4)^{3}(0.6)^{4}.

Worth noting

7C3 (0.6)3(0.4)4{}^{7}C_{3}\,(0.6)^{3}(0.4)^{4} gives the success power to the failures: it is P(X=4)P(X = 4).

Concept
Writing the binomial formula
Typical time
90 s
Your time
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The rule this testsBinomial probabilities
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Ten questions from Binomial & Poisson Distributions, at your own pace.

Practise this chapter →

Ten questions from Binomial & Poisson Distributions, at your own pace.