a bag contains 30 cards having the numbers 1 to 30 if one card is drawn at random from the bag then find the probability of the following events 1) The number on the card is prime 2)The number on the card is perfect square
Answers
Answer:
Solution(i):
Let E be the event of drawing a number not divisible by 3 from the cards numbered 1 to 30
Numbers not divisible by 3 from 1 to 30=1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29
No. of favorable outcomes=20
Total no. of possible outcomes =30
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
30
20
=
3
2
Therefore, the probability of drawing a number not divisible by 3 from the cards numbered 1 to 30=
3
2
Solution(ii):
Let F be the event of drawing a prime number greater than 7 from the cards numbered from 1 to 30
Prime numbers greater than 7 from 1 to 30=11,13,17,19,23,29
No. of favorable outcomes=6
Total no. of possible outcomes =30
We know that, Probability P(F) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
30
6
=
5
1
Therefore, the probability of drawing a prime number greater than 7 from the cards numbered 1 to 30=
5
1
Solution(iii):
Let G be the event of drawing a non-perfect square number from the cards numbered from 1 to 30
Non-Perfect square numbers from 1 to 30=2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27,28,29,30
No. of favorable outcomes=25
Total no. of possible outcomes =30
We know that, Probability P(G) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
30
25
=
6
5
Therefore, the probability of drawing a non-perfect square number from the cards numbered 1 to 30=
6
5
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