Question

The probabilities that students A, B and C can solve a particular problem are 2/5, 2/3, and 1/2 respectively. If they all try, determine the probability that at least one of the group solves the problems

Answer 1

Lets look at the probability that none of the 3 students solves the problem, P0.
The probability that student A does not solve the problem is given by:
\[\large P _{A_0}=1-\frac{2}{5}=\frac{3}{5}\]
The probability that student B does not solve the problem is given by:
\[\large P _{B_0}=1-\frac{2}{3}=\frac{1}{3}\]
The probability that student C does not solve the problem is given by:
\[\large P _{C_0}=1-\frac{1}{2}=\frac{1}{2}\]
The events 'A does not solve the problem', 'B does not solve the problem' and 'C does not solve the problem' are independent. Therefore the probability that none of the 3 students solves the problem is given by:
\[\large P _{0}=P _{A_0}\times P _{B_0}\times P _{C_0}=\frac{3}{5}\times\frac{1}{3}\times\frac{1}{2}\]
Therefore the probability that at least one of the group solves the problems is given by:
\[\large P(1\ or\ more\ solves)=1-P _{0}\]