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Question: There are 4 seats in a car. Using a tree diagram, find the probability that 2 boys and 2 girls are seated in the car.
A ) 32
B ) 38
C ) 58
D ) 35
Steps to derive
1 The tree diagram showing all the possible ways in which girls and boys can be seated in the 4 seats available is as shown below
2 From the tree diagram there are 16 possible outcomes.
3 2 boys and 2 girls can be seated in 4 seats in 6 different ways
BBGG BGBG BGGB GBBG GGBB GBGB
4 So, there are 6 favorable outcomes.
5 P(2 boys and 2 girls) = Number of favorable outcomes / Number of possible outcomes = 616 = 38
[Substitute and simplify.]
Hence the right answer is Option B
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