Question

Bag A contains $3$ Red Marbles and $4$ Blue Marbles.
Bag B contains $5$ Red Marbles and $3$ Blue Marbles.
A marble is taken from each bag in turn .
What is the probability of getting a blue marble followed by a red taking first ball from bag $A$ and second from bag $B$?

• A. $\frac{5}{14}$
• B. $\frac{3}{14}$
• C. $\frac{8}{14}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{14}$

The probability of getting a blue marble from bag A is $\frac{4}{3+4}=\frac{4}{7}$

And the probability of getting a red marble from bag B is $\frac{5}{5+3}=\frac{5}{8}$

$\Rightarrow$ probability of getting a blue marble followed by a red becomes $\frac{4}{7}\times \frac{5}{8}=\frac{5}{14}$