A bag contains 4 white marbles and 3 blue marbles. Another bag contains 5 red and 6 blue marbles. If a marble is picked at random from each bag, find the probability that they are of the same colour.
A
\(\frac{9}{11}\)
B
\(\frac{18}{77}\)
C
\(\frac{1}{2}\)
D
\(\frac{11}{12}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
1st bag → 4 W, 3 B = 7 marbles
2nd bag → 5 R, 6 B = 11 marbles
The only possible way of picking marbles of the same colour is to pick a blue marble from each bag
therefore, Pr( same colour) = \(\frac{3}{7}\times \frac{6}{11} = \frac{18}{77}\)
Source: Myschool Past Questions Archive (Record #69143)