A bag contains 7 red balls, 11 yellow balls, and 4 pink balls. If two balls are drawn at random from the bag, one after another, what is the probability that the first ball is red and the second ball is yellow?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{1}{6}\)
The balls are drawn one after another, and since the question does not say that the first ball is replaced, it is not put back: the second draw is made from one ball fewer. The probability of both events is the product of the probability of the first and the probability of the second after the first has happened.
Total number of balls: \(7+11+4=22\)
First ball red: \(\displaystyle\frac{7}{22}\)
Second ball yellow, from the 21 balls left (all 11 yellow still there): \(\displaystyle\frac{11}{21}\)
Both events together: \(\displaystyle\frac{7}{22}\times\frac{11}{21}=\frac{1}{6}\)