Cards numbered from 1 to 60 are kept in a box. if a card is drawn at random from the box. The probability that the number on the drawn card is divisible by 3
Answers
Step-by-step explanation:
Solution(i):
Let E be the event of drawing a number from the cards numbered from 11 to 60
Odd numbers from 11 to 60=11,13,15,.....,89
No. of favorable outcomes=25
Total no. of possible outcomes =50
We know that, Probability P(E) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
50
25
=
2
1
Therefore, the probability of an odd number from the cards numbered 11 to 60=
2
1
Solution(ii):
Let F be the event of drawing a perfect square number from the cards numbered from 11 to 60
Perfect square numbers from 11 to 60=16,25,36,49
No. of favorable outcomes=4
Total no. of possible outcomes =50
We know that, Probability P(F) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
50
4
=
25
2
Therefore, the probability of drawing a perfect square number from the cards numbered from 11 to 60=
25
2
Solution(iii):
Let G be the event of drawing a number divisible by 5 from the cards numbered from 11 to 60
Numbers divisible by 5 from 11 to 60=15,20,25,30,35,40,45,50,55,60
No. of favorable outcomes=10
Total no. of possible outcomes =50
We know that, Probability P(G) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
50
10
=
5
1
Therefore, the probability of drawing a number divisible by 5 from the cards numbered from 11 to 60=
5
1
Solution(iv):
Let H be the event of drawing a prime number less than 20 from the cards numbered from 11 to 60
Prime numbers less than 20 from 11 to 60=11,13,17,19
No. of favorable outcomes=4
Total no. of possible outcomes =50
We know that, Probability P(H) =
(Total no.of possible outcomes)
(No.of favorable outcomes)
=
50
4
=
25
2
Therefore, the probability of drawing a prime number less than 20 from the cards numbered from 11 to 60=
25
2