Exercise · ZW-CONDITIONAL-PROBABILITY-007 · ★★☆ Intermediate

A family has two children and at least one is a girl. Assuming each child is equally likely to be a boy or a girl, what is the probability that both are girls?

Choose one option.

Show answer

C. 1/3

Explanation

The cases with at least one girl are GG, GB, BG (3, equally likely); only GG has two girls. The probability is \(1/3\), not \(1/2\).

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Review the concept: Conditional probability

The conditional probability of \(A\) given \(B\), \(P(A\mid B)\), is the probability that \(A\) occurs when \(B\) is already known to have occurred; it is computed within the space reduced to \(B\).

\[P(A\mid B)=\frac{P(A\cap B)}{P(B)},\qquad P(B)>0\]

More practice problems: conditional probability

ZW-CONDITIONAL-PROBABILITY-001 If P(A∩ B)=0.2 and P(B)=0.5, what is P(A| B)?
ZW-CONDITIONAL-PROBABILITY-002 A fair die is rolled and it is known the result is even. What is the probability that it is 6?
ZW-CONDITIONAL-PROBABILITY-003 Two fair dice are rolled and the first shows 3. What is the probability that the sum is 8?
ZW-CONDITIONAL-PROBABILITY-004 If P(A)=0.6, P(B)=0.4 and P(A∪ B)=0.7, what is P(A| B)?
ZW-CONDITIONAL-PROBABILITY-005 An urn has 5 red and 3 blue balls. Two are drawn without replacement. Given that the first was red,…
ZW-CONDITIONAL-PROBABILITY-006 Two cards are drawn from a 52-card deck without replacement. What is the probability that both are…
ZW-CONDITIONAL-PROBABILITY-008 If P(A)=0.4 and P(B| A)=0.5, what is P(A∩ B)?
ZW-CONDITIONAL-PROBABILITY-009 With P(B)>0, which statement is true?