Answer:

1,8/20

2.8/20

Step-by-step explanation:

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MATHS

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is

(i) divisible by 2 or 3 (ii) a prime number

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ANSWER

Solution(i):

Let E be event of drawing a card with number divisible by 2 or 3 from the cards with numbers 1 to 20

Numbers divisible by 2 or 3 from 1 to 20=2,3,4,6,8,9,10,12,14,15,16,18,20

No. of favorable outcomes=13

Total no. of possible outcomes =20

We know that, Probability P(E) =

(Total no.of possible outcomes)

(No.of favorable outcomes)

=

20

13

Therefore, the probability that a number on the card selected from numbers 1 to 20 divisible by 2 and 3 is

20

13

Solution(ii):

Let F be event of drawing a card with prime number from the cards with numbers 1 to 20

Prime numbers from 1 to 20=2,3,5,7,11,13,17,19

No. of favorable outcomes=8

Total no. of possible outcomes =20

We know that, Probability P(F) =

(Total no.of possible outcomes)

(No.of favorable outcomes)

=

20

8

=

5

2

Therefore, the probability that a card with prime number is selected from numbers 1,2,3,...,20 =

5

2