Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is
(i)not divisible by 3
(ii)a prime number greater than 7
(iii)not a perfect square number
Answers
SOLUTION :
Given : Cards marked with numbers from 1 to 30
Total number of outcomes = 30
(i)Let E1 = Event of getting a number not divisible by 3
Numbers which are not divisible by 3 = 1,2,4, 5, 7,8, 10,11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26,28, 29
Number of outcome favourable to E1 = 20
Probability (E1) = Number of favourable outcomes / Total number of outcomes
P(E1) = 20/30 = ⅔
Hence, the required probability of getting a number not divisible by 3 , P(E1) = 2/3 .
(ii) Let E2 = Event of getting a prime number greater than 7
prime number greater than 7 =11,13,17,19,23,29
Number of outcome favourable to E2 = 6
Probability (E2) = Number of favourable outcomes / Total number of outcomes
P(E2) = 6/30 = 1/5
Hence, the required probability of getting a prime number greater than 7 , P(E2) = ⅕ .
(iii)Let E3 = Event of getting a number which are not perfect squares
Numbers which are perfect squares = 1, 4, 9, 16, 25
Number of perfect squares = 5
Numbers which are which are not perfect squares = 30 - 5 = 25
Number of outcome favourable to E3 = 25
Probability (E3) = Number of favourable outcomes / Total number of outcomes
P(E3) = 25/30 = 5/6
Hence, the required probability of getting a number which are not perfect squares , P(E3) = 5/6 .
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P(E)=favourable outcome/total number of outcome
1) favourable outcome are, =20
P(E)=20/30
2)6/30
3)25/30