Question

cards market with numbers 2 to 101 are placed in a box and mixed thoroughly.one card is drawn from this box find the probability that the number on the card is...a)a number less than 14.b) a number which is a perfect square.c) a prime number less than 20

Answer 1

Space =  {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100, 101}
n=100

a.) Positive Outcomes = {2,3,4,5,6,7,8,9,10,11,12,13};
     m =12
     P(less than 14) = m/n = 12/100 = 6/50 = 3/25

b.) Positive Outcomes = {4,9,16,25,36,49,64,81,100}
     m = 9
     P(perfect square) = m/n = 9/100

c.) Positive Outcomes = {2,3,5,7,11,13,17,19}
     m = 8
     P(prime no. less than 20) = m/n = 8/100 = 4/50 = 2/25

Answer 2

number of cards from 2 to 101=100
a)numbers less than 14 are 2,3,4,5,6,7,8,9,10,11,12,13
favourable outcomes/number of cards
=12/100

b)perfect squares are 4,9,16,25,36,49,64,81,100
favourable outcomes/number of cards
=9/100

c)prime numbers less than 20 are 2,3,5,7,11,13,17,19
favourable outcomes /number of cards
=8/100
=2/25