A bag contains 5 black, 3 white and 2 red balls. Three balls are drawn in succession. What is the probability that the first ball is red, the second ball is black and the third ball is white?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{1}{24}\)
The balls are drawn in succession and nothing is said about putting them back, so they are drawn without replacement: each draw changes what is left in the bag and the probabilities of the three draws are multiplied. The bag has \(5+3+2=10\) balls.
First ball red: 2 red out of 10, so \(\displaystyle\frac{2}{10}\)
Second ball black: 5 black out of the 9 left, so \(\displaystyle\frac{5}{9}\)
Third ball white: 3 white out of the 8 left, so \(\displaystyle\frac{3}{8}\)
Probability \(\displaystyle=\frac{2}{10}\times\frac{5}{9}\times\frac{3}{8}=\frac{30}{720}=\frac{1}{24}\)