Question : Cards marked with numbers 3,4,5. . .50 are placed in a bag and mixed thoroughly. One card is drawn at random from the bag. Find the probability that number on the card drawn is
a) divisible by 7.
b) a perfect square.
c) a multiple of 6.
Doubt by Pari
Solution :
Total Number of cards = {3,4,5,. . .50}
= 50-3+1 = 48
P(E) = No. of favorable outcomes / No. of total possible outcomes
i) No which is divisible by 7 between 3 and 50
{7,14,21,28,35,42,49} = 7
P(divisible by 7) = 7/48
ii) No. on the card which is a perfect square
{2², 3², 4², 5², 6², 7²}
{4, 9, 16, 25, 36, 49} = 6
[Note : Perfect squares are those numbers whose square root is a perfect integer.]
P(Perfect Squares) = 6/48 = 1/8
iii) No. on the card which is a multiple of 6
{6,12,18,24,30,36,42,48} = 8
P(a multiple of 6) = 8/48 = 1/6
Similar Question
Cards marked with numbers 3,4,5. . .50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected cards bear a perfect square number.