Probability Question 11
Question 11 - 31 January - Shift 1
A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is
(1) $\frac{5}{7}$
(2) $\frac{2}{7}$
(3) $\frac{3}{7}$
(4) $\frac{5}{6}$
Show Answer
Answer: (1)
Solution:
Formula: Conditional Probability, Bayes’ Theorem
$\frac{{ }^{5} C_2+{ }^{6} C_2}{{ }^{2} C_2+{ }^{3} C_2+{ }^{4} C_2+{ }^{5} C_2+{ }^{8} C_2}=\frac{10+15}{1+3+6+10+15}$
$=\frac{25}{35}=\frac{5}{7}$
Therefore, the probability that the bag contains at least 5 black balls is $\frac{5}{7}$.
