question_answer

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

Answer:

Total number of outcomes \[=20\]

(i) Let \[{{E}_{1}}\] be the event of getting a number divisible by 2 or 3.

Then, favourable outcomes = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 3, 9, 15.

Number of favourable outcomes \[=13\]

\[\therefore \] P (getting a no. divisible by 2 or 3)

\[=P({{E}_{1}})=\frac{13}{20}\]

(ii) Let \[{{E}_{2}}\] be the event of getting a prime number. Then, favourable outcomes = 2, 3, 5, 7, 11, 13, 17, 19.

Number of favourable outcomes \[=8\]

P (getting a prime number) \[=P({{E}_{2}})=\frac{8}{20}=\frac{2}{5}\]