question_answer

All red face cards are removed from a pack of playing cards. The remaining cards were well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is:

(i) a red card

(ii) a face card

(iii) a card of clubs

Answer:

Total number of possible outcomes \[=52-6=46\]

[\[\because \] No. of red face cards \[=6\]]

(i) Let \[{{E}_{1}}\] be the event of getting a red card.

Favourable outcomes = 10 of heart + 10 of diamond

\[\therefore \] No. of favourable outcomes \[=20\]

\[\therefore \] P (getting a red card) \[=P({{E}_{1}})=\frac{20}{46}=\frac{10}{23}\]

(ii) Let \[{{E}_{2}}\] be the event of getting a face card

Favourable outcomes \[=3\]of club + 3 of spade

\[\therefore \] No. of favourable outcomes \[=6\]

\[\therefore \]P (getting a face card) \[=P({{E}_{2}})=\frac{6}{46}=\frac{3}{23}\]

(iii) Let \[{{E}_{3}}\] be the event of getting a card of clubs Favourable outcomes \[=13\] of clubs

\[\therefore \] No. of favourable outcomes \[=13\]

\[\therefore \] P (getting a card of clubs) \[=P({{E}_{3}})=\frac{13}{46}\]