51 women wore coloured shoes to a party, out of which 21 wore purple and 9 wore white. if a woman is selected…

Analyze the question: We need the probability that a randomly chosen woman wears neither purple nor white shoes.

Concept: If the groups don't overlap, then P(neither) = (Total − purple − white) ÷ Total. This assumes nobody wears both colours, which is reasonable here because each woman wore one pair of coloured shoes.

Solution:

• Total women = 51
• Purple = 21
• White = 9
• Purple or white = 21 + 9 = 30
• Neither = 51 − 30 = 21

P(neither) = 21/51 = 7/17

Check: 21 ÷ 3 = 7 and 51 ÷ 3 = 17, so 21/51 simplifies to 7/17.

Answer: B

Tip: For "neither... nor" questions, subtract everything that is counted from the total, then divide by the total. Always simplify the fraction at the end, since the options are usually in lowest terms. Here, dividing top and bottom by 3 gave the option directly.