A box contains 70 marbles of different colours i.e. purple, pink and blue. Find the number of pink marbles in the box, if probability of picking up a purple marble is \(\frac{3}{7}\)and that of either a purple or a pink marble is \(\frac{4}{7}\).
Answer & explanation
Correct answer: option 4
Probability of picking a purple marble = \(\frac{No.\;of\;purple\;marbles}{Total\;number\;of\;marbles}\)
Probability of picking a purple marble = \(\frac{3}{7}\)
⇒ \(\frac{3}{7}\) = \(\frac{No.\;of\;purple\;marbles}{70}\)
No. of purple marbles = 30
Probability of picking either a purple or pink marble = \(\frac{4}{7}\)
Probability of picking either a purple or pink marble =
\(\frac{No.\;of\;purple\;or\;pink\;marbles}{Total\;No.\;of\;marbles}\)
Let number of pink marbles= x
∴ \(\frac{x\;+\;30}{70}\) = \(\frac{4}{7}\)
⇒ x = 10
Hence, option D is correct.