A bag contains $20$ balls. Some of the balls are red, some are yellow and the rest are blue. Two b

Question

A bag contains $20$ balls. Some of the balls are red, some are yellow and the rest are blue. Two balls are taken, at random and at the same time, from the bag. The probability that one of the balls is red and the other one is yellow is $\dfrac{28}{95}$. The probability that one of the balls is red and the other one is blue is $\dfrac{4}{19}$. Determine the number of red balls originally in the bag.[5] Events $A$ and $B$ are such that $\mathrm{P}(A\cap B')=0.364$, $\mathrm{P}(A'\cap B)=0.124$ and $\mathrm{P}((A\cup B)')=0.276$. Show that $A$ and $B$ are not mutually exclusive events.[2] Determine whether $A$ and $B$ are independent events.[2]

Accepted Answer

(a) $8$ (b)(i) $\mathrm{P}(A\cap B)=0.236\neq 0$ (ii) $\mathrm{P}(A)\mathrm{P}(B)=0.6\times 0.36=0.216\neq 0.236$, so $A$ and $B$ are not independent

N2026 P2 Q7

N2026 P2 Q7