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Random Variables, Expectation & Variance · Question 26 of 68

Question 26

MediumOriginal question

In families with 3 children, a boy and a girl are equally likely at each birth. XX is the number of girls. What is P(X≥2)P(X \ge 2)?

Options for question 26

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. P(X=2)=38P(X = 2) = \frac{3}{8} (GGB, GBG, BGG) and P(X=3)=18P(X = 3) = \frac{1}{8}.

  2. P(X≥2)=38+18=12P(X \ge 2) = \frac{3}{8} + \frac{1}{8} = \frac{1}{2}.

Worth noting

38\frac{3}{8} is P(X=2)P(X = 2) alone; 'at least 2' includes 3 girls.

Concept
The probability of a range of values
Typical time
90 s
Your time
—
The rule this testsProbability distributions
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Ten questions from Random Variables, Expectation & Variance, at your own pace.

Practise this chapter →

Ten questions from Random Variables, Expectation & Variance, at your own pace.