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) \[=P({{E}_{3}})=\frac{13}{46}\]
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