Question-8

\(57\%\) students of girls’ school wear neither a ring nor a necklace, \(30\%\) wear a ring, and \(25\%\) wear a necklace. If one of them is randomly chosen, find the probability that she is wearing a ring and a necklace.

Hint

Use addition rule of probability.

Answer

0.12

Solution

Define event \(R\) as “wears a ring” and the event \(N\) as “wears a necklace”. Given,

\(P(R^c \cap N^c) = P(R \cup N)^c = 0.57 \implies P(R \cup N) = 1 - P(R \cup N)^c = 1-0.57 = 0.43,\) \(P(R) = 0.30\) and \(P(N) = 0.25\)

\(P(R \cup N) = P(R) + P(N) - P(R \cap N)\)

\(P(R \cap N) = P(R) + P(N) - P(R \cup N) = 0.30+0.25-0.43 = 0.12\)