INSTRUCTION: From the words lettered A-D choose the appropriate answer
A bag contains three red and five white balls of equal size. Two balls are picked at random one after the other without replacement. What is the probability that both balls are of the same colour.
A. \(13 / 32\) B. \(3 / 28\) C. \(5 / 14\) D. \(13 / 28\)
Correct Answer: D
Explanation
No of Red balls \(=3\) No of white balls \(=\frac{5}{8 \text { balls }}\) \(P\left(\begin{array}{c}\text { both balls } \\ \text { of the } \\ \text { same } \\ \text { colour }\end{array}\right)=P\left(\begin{array}{l}\text { lst ball } \\ W \text { and } \\ 2 n d ~ W\end{array}\right)\) or \(P\left(\begin{array}{l}1 \text { st ball } \\ R \text { and } 2 n d ~\end{array}\right)\) \(=\mathrm{P}(\mathrm{WW})\) or \(\mathrm{P}(\mathrm{RR})\) \(=\frac{5}{8} \times \frac{4}{7}+\frac{3}{8} \times \frac{2}{7}\) \(=\frac{20}{56}+\frac{6}{56}=\frac{26}{56}=\frac{13}{28}\)
