question_answer

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card

(i) is divisible by 9 and is a perfect square,

(ii) is a prime number greater than 80.

Answer:

Number of possible outcomes \[=100\]

(i) Let \[{{E}_{1}}\] be the event of getting a number divisible by 9 and is a perfect square.

\[\therefore \] Favourable outcomes \[=\{9,36,81\}\]

Number of favourable outcomes \[=3\]

\[\therefore P({{E}_{1}})=\frac{3}{100}\]

(ii) Let \[{{E}_{2}}\] be the event of getting a prime number greater than 80.

\[\therefore \] Favourable outcomes \[=\{83,89,97\}\]

Number of favourable outcomes \[=3\]

\[\therefore P({{E}_{2}})=\frac{3}{100}\]