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
Step-by-step explanation:
1 ) Total outcomes = 30
Favourable outcomes of getting a prime number greater than 7 = 6 { 11, 13, 17, 19, 23, 29 }
P ( x ) = Favourable outcomes / Total outcomes
P ( getting a prime number greater than 7 ) = 6 / 30 = 1 / 5
2 ) Total outcomes = 30
Favourable outcomes of getting not a perfect square = 25 { 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 }
P ( x ) = Favourable outcomes / Total outcomes
P ( getting not a perfect square ) = 25 / 30 = 5 / 6
Answer:
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
hope it will help you.........❣️