If 90% of the customers has life insurance and 80 % has motor insurance, how many have both? An insurance company has only two types of insurances, life and motor. If we know that 80 % of the policy holders has life insurance and 90 % has motor insurance, is it possible to calculate what fraction of policy holders that owns both types of insurances? I want to check if my attempt is correct: Denote $L$ - has life insurance, $M$ - has motor insurance. $$ 1 = P(L \cup M) = P(M) + P(L) - P(M \cap L ) = 1,7 - P(M \cap L). $$ Hence, 70 % of the policyholders has both insurances.

Answer looks right but I'm having trouble following the work, what with the comma and the 7.

$$ P(M\cap L) = P(M) + P(L) - P(M\cup L),$$ where $P(M) = 0.9$ and $P(L) =0.8$. Also, $P(M \cup L) = 1$ because there are only two types of insurance. Plug in these values to get the answer.