Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box . Find the probability that number of the is : a) An even numberb) A number less than 14 c) A number which is a perfect squared) A prime number less than 20
Answers
Answer:There are 100 cards in the box out of which one card can be drawn in 100 ways.
Total number of elementary events=100
a)From no.s 2 to 101,there are 50 even no.s.
Favourable no. of elementary events=50
P(getting an even no. card)=50/100=1/2
b)There are 12 cards bearing no.s less than 14.
Favourable no. of elementary events=12
P(getting a no. less than 14)=12/100=3/25
c)Those no.s from 2 to 101 which are perfect squares are 4,9,16,25,.......,100 i.e. squares of 2,3,4,5,.......,10 respectively.Therefore there are 9 cardsmarked with the no.s which are perfect squares.
Favourable no. of elementary events=9
P(getting a no. which is a perfect square)=9/100
d)Prime no.s less than 20 in the no.s from 2 to 101 are 2,3,5,7,11,13,17 and 19.
Thus,there are 8 cards marked with prime no.s less than 20.
Favourable no. of elementary events=8
P(getting a prime no. less than 20)=8/100=2/25.
Given : Cards marked with number 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box
To Find : probability that the number on the card:
a) An even number
b) A number less than 14
c) A number which is a perfect square
d) A prime number less than 20
Solution:
Cards marked with number 2 to 101
=> Total Card = 100
n(S) = 100
An even number
A = { 2 , 4 , 6 , ..............................., 100 }
=> n(A) = 50
probability that the number on the card even number = n(A)/n(S)
= 50/100
= 1/2
A number less than 14
B = { 2 , 3 , 4 , ......................., 13}
n(B) = 12
probability that the number on the card is less than 14 = 12/100
= 3/25
A number which perfect square
Perfect square = {2² , 3² ,............................9² , 10² }
n(C) = 9
probability that the number on the card is perfect square = 9/100
A prime number less than 20
D= {2,3 ,5 , 7 , 11 , 13 , 17 , 19 }
n(D) = 8
probability that A prime number less than 20 = 8/100
= 2/25
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