During summer break, Harish wanted to play with his friends but it was too hot outside, so he decide

Question

During summer break, Harish wanted to play with his friends but it was too hot outside, so he decided to play some indoor game with his friends. He collects 20 identical cards and writes the numbers 1 to 20 on them (one number on one card). He puts them in a box. He and his friends make a bet for the chances of drawing various cards out of the box. Each was given a chance to tell the probability of picking one card out of the box.\ Based on the above information, attempt any 4 questions out of 5 .\ The probability that the number on the card drawn is a multiple of 3,6 and 9 is\

Professor PC Thomas Classes · Answer

(a):Card numbered from $\{1,2,3, \ldots ., 20\}$\ Total number of possible outcomes $=20$
 Multiple of $3=\{3,6,9,12,15,18\}$ Multiple of $6=\{6,12,18\}$\ Multiple of $9=\{9,18\}$\ Multiple of 3, 6, 9, $=18$\ ∴ Total number of favourable outcomes $=1$\ Hence the probability that the card is a multiple of 3,6 and\ $9=\frac{1}{20}$\ ∴ Required Probability $=\frac{1}{20}$\