question_answer

A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is:

(i) divisible by 3 or 5

(ii) a perfect square number.

Answer:

Total number of possible outcomes \[=25\]

(i) Let \[{{E}_{1}}\] be the event of getting a number divisible by 3 or 5.

Favourable outcomes = {3, 6, 9, 12, 15, 18, 21, 24, 5, 10, 20, 25}

\[\therefore \] Number of favourable outcomes \[=12\]

P (getting a no. divisible by 3 or 5) \[=P({{E}_{1}})=\frac{12}{25}\]

(ii) Let \[{{E}_{2}}\] be the event of getting a perfect square number.

Favourable outcomes= {1, 4, 9, 16, 25}

\[\therefore \] Number of favourable outcomes \[=5\]

P (getting a perfect square number) \[=P({{E}_{2}})=\frac{5}{25}=\frac{1}{5}\]