A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears
(i) a two digit number
(ii) a number which is a perfect square
Answers
Probability of getting a two-digit number = 81/89
Probability of getting a perfect square = 8/89
Step-by-step explanation:
A bag contains cards which are numbered from 2 to 90.
Total number of outcomes = 89
(i) two-digit number.
Number of unfavorable outcomes = 8
So Number of favorable outcomes = 89 - 8 = 81
Probability of getting a two-digit number = 81/89
(ii) Number which is a perfect square.
Number of favorite squares between 2 and 90 = 8
(4, 9, 16, 25, 36, 49, 64, 81)
Probability of getting a perfect square = 8/89
SOLUTION :
Given : Cards marked with numbers from 2 to 90
Total number of outcomes = 90 - 2 + 1 = 89 ( both 2 & 90 are included)
(i)Let E1 = Event of getting a two digit number
Numbers which are 2 digits are from 10 to 90 = 90 - 10 + 1 = 81 ( both 10 & 90 are included)
Number of outcome favourable to E1 = 81
Probability (E1) = Number of favourable outcomes / Total number of outcomes
P(E1) = 81/89
Hence, the required probability of getting two digit number, P(E1) = 81/89 .
(ii)Let E2 = Event of getting a number which are perfect squares
Numbers which are perfect squares = 4, 9, 16, 25 ,35,49,64, 81
Number of perfect squares = 8
Number of outcome favourable to E2 = 8
Probability (E2) = Number of favourable outcomes / Total number of outcomes
P(E2) = 8/89
Hence, the required probability of getting a number which are perfect squares ,P(E2) = 8/89 .
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