Cards numbered 1 to 30 are put in a bag. A card is drawn at random fro

1.	Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the 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.
Answer» Cards numbered 1 to 30 are put in a bag. So, total number of cards = 30 (i) Numbers divisible by 3 form 1 to 30 = {3,6,9,12,15,18,21,24,27,30} Total numbers divisible by 3 = 10 Numbers not divisible by 3 = 30 – 10 = 20 P(drawn card is not divisible by 3) = 20/30 = 2/3 (ii) A prime numbers greater than 7 form 1 to 30 = {11, 13, 17, 19, 23, 29} Total prime number greater than 7 = 6 P(drawn card is a prime number greater than 7) = 6/30 = 1/5 (iii) Perfect square numbers form 1 to 30 = {1,4,9,16,25} Number of Perfect square = 5 Non perfect square numbers = 30-5 = 25 P(drawn card is not a perfect square number) = 25/30 = 5/6

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the 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.

Answer»

Cards numbered 1 to 30 are put in a bag.

So, total number of cards = 30

(i) Numbers divisible by 3 form 1 to 30 = {3,6,9,12,15,18,21,24,27,30}

Total numbers divisible by 3 = 10

Numbers not divisible by 3 = 30 – 10 = 20

P(drawn card is not divisible by 3) = 20/30 = 2/3

(ii) A prime numbers greater than 7 form 1 to 30 = {11, 13, 17, 19, 23, 29}

Total prime number greater than 7 = 6

P(drawn card is a prime number greater than 7) = 6/30 = 1/5

(iii)

Perfect square numbers form 1 to 30 = {1,4,9,16,25}

Number of Perfect square = 5

Non perfect square numbers = 30-5 = 25

P(drawn card is not a perfect square number) = 25/30 = 5/6

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