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 marble of each colour?

• A. $\frac{19}{56}$
• B. $\frac{28}{56}$
• C. $\frac{31}{56}$
• D. None of these

Answer 1

The correct option is D None of these

Total marbles in bag A: $3R+4B=7$

Total marbles in bag B: $5R+3B=8$

Now a marble has been taken from each bag in turn:

Total cases: (Red from A and Blue from B) or (Blue from A and Red from B)

$=\frac{3}{7}\times \frac{3}{8}+\frac{4}{7}\times \frac{5}{8}$

$=\frac{9}{56}+\frac{20}{56}$ $=\frac{29}{56}$