From the bag containing three red and four white balls, a ball is picked but not replaceD. A second ball is then pickeD. Find the probability that the balls are of the same color
A. \(\frac{1}{3}\) B. \(\frac{9}{49}\) C. \(\frac{3}{7}\) D. \(\frac{1}{7}\)
Correct Answer: C
Explanation
It is either the two balls are red or they are white. Hence, \(P_{\text {(ramr coliour) }}=P_{\text {(ifiss red second red }}+P_{(\text {first white, second whice) }}\) Number of red balls \(=3\) Number of white balls \(=4\) Keep in mind that the selection is without replacement. Then, \(P\) (saine colour \()=\left(\frac{3}{7} \times \frac{2}{6}\right)+\left(\frac{4}{7} \times \frac{3}{6}\right)\) \(=\frac{1}{7}+\frac{2}{7}=\frac{3}{7}\)
