51 women wore coloured shoes to a party, out of which 21 wore purple and 9 wore white. if a woman is selected at Random. What is the probability that she is wearing neither a purple shoe nor a white shoe?
A. \(\frac{10}{17}\) B. \(\frac{7}{17}\) C. \(\frac{20}{51}\) D. \(\frac{3}{17}\) E. \(\frac{1}{51}\)
Correct Answer: B
Explanation
No of women wearing both purple and white shoes = 21 + 9 = 30 women. No of women wearing neither purple nor white shoes = 51 - 30 = 21 women \(\therefore\) Probability of picking a woman wearing neither purple nor white shoes = \(\frac{21}{51}\) = \(\frac{7}{17}\).
