A box has cards numbered 10 to 55. Cards are mixed thoroughly and a card is
drawn at random from the box. Find the probability that the card drawn from
the box has:
(i)a perfect square.
(ii) divisible by 5 and 6.
(iii) divisible by 3 or 5.
Answers
P(A) = n(A) / n(S) = 43/86Total no. of cards = 86, i.e., n(S) = 86
(i) Let A be the favourable outcomes of getting an odd number. Then,
A = {15,17,19,21,23,25,27,29,31,33,35, 37, 39,41,43,45,47,49, 51,53, 55,57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99}
n( A) = 43
Therefore,
straight P left parenthesis straight A right parenthesis equals space fraction numerator straight n open parentheses straight A close parentheses over denominator straight n open parentheses straight S close parentheses end fraction equals 43 over 86 space equals space 1 half
(ii) Let B be the favourable outcomes of getting perfect square number. Then,
B = {16, 25,36, 49, 64,81) i.e., n(B) = 6
Therefore,
P left parenthesis B right parenthesis equals fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals 6 over 86 space equals space 3 over 43
(iii) Let C be the favourable outcomes of getting a number divisible by 7. Then
C = {14,21,28,35,42,49,56,63,70,77,84, 91,98}
i.e., n( C) = 13
Therefore,