# Solved: A recent survey conducted by Towers Perrin and published in the Financial Times showed that among 460 organizations in 13 European countries

#### ByDr. Raju Chaudhari

Feb 26, 2021

A recent survey conducted by Towers Perrin and published in the Financial Times showed that among 460 organizations in 13 European countries, 93% have bonus plans, 55% have cafeteria-style benefits, and 70% employ home-based workers. If the types of benefits are independent, what is the probability that an organization selected at random will have at least one of the three types of benefits?

#### Solution

Let $A$ denote organizations have bonus plan, $P(A)=0.93$. So $P(A')=1- 0.93 = 0.07$.

Let $B$ denote organizations have Cafeteria-style benefits, $P(B) =0.55$. So $P(B')=1- 0.55 = 0.45$.

Let $C$ denote organizations have employ home-based workers, $P(C) =0.70$. So $P(C')=1- 0.70 = 0.3$.

The probability that an organization selected at random have at least 1 of the three types of benefits is equal to 1 minus the probability that none of the benefits.

The probability that an organization selected at random will have none of the benefits = $P(A'\cap B' \cap C')$.

Thus

 \begin{aligned} P(A'\cap B' \cap C') &= P(A')*P(B')*P(C')\\ &= 0.07 * 0.45 * 0.3\\ &= 0.00945 \end{aligned}

The probability that an organization selected at random will have at least 1 of the three types of benefits is

$= 1- P(A'\cap B' \cap C') =1- 0.00945= 0.99055$.