Multiple choice

Three groups of children contain 3 girls and one boy; 2 girl and 2 boys, one girl and 3 boys. One child is selected at random from each group. Show that the chance that the three selected consist of 1 girl and 2 boys is

  1. $\dfrac{13}{36}$
  2. $\dfrac{13}{32}$
  3. $\dfrac{15}{32}$
  4. $\dfrac{15}{36}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Probabilities of picking a girl from each group: G1=3/4, G2=2/4, G3=1/4. Probabilities of picking a boy: B1=1/4, B2=2/4, B3=3/4. We need 1 girl and 2 boys. Possible cases: (G,B,B) = 3/4 * 2/4 * 3/4 = 18/64; (B,G,B) = 1/4 * 2/4 * 3/4 = 6/64; (B,B,G) = 1/4 * 2/4 * 1/4 = 2/64. Sum = 26/64 = 13/32.

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