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All the three face cards of spades are removed from a well shuffled pack of \[\mathbf{52}\]cards. A card is then drawn at random from the remaining pack. Find the probability of getting: \[\left( \mathbf{i} \right)\] a black face card \[\left( \mathbf{ii} \right)\]a queen
All the three face cards of spades are removed from a well shuffled pack of \[\mathbf{52}\]cards. A card is then drawn at random from the remaining pack. Find the probability of getting: \[\left( \mathbf{i} \right)\] a black face card \[\left( \mathbf{ii} \right)\]a queen
CBSE | Class 10 | Exercise 13.3 | Selina | Statistics and Probability
All the three face cards of spades are removed from a well shuffled pack of \[\mathbf{52}\]cards. A card is then drawn at random from the remaining pack. Find the probability of getting: \[\left( \mathbf{i} \right)\] a black face card \[\left( \mathbf{ii} \right)\]a queen

Solution:

We have,

Total number of cards \[=\text{ }52\]

If \[3\] face cards of spades are removed

Then, the remaining cards \[=\text{ }52\text{ }\text{ }3\text{ }=\text{ }49\text{ }=\] number of possible outcomes

So\[,\text{ }n\left( S \right)\text{ }=\text{ }49\]

\[\left( i \right)\] Number of black face cards left \[=\text{ }3\]face cards of club

Event of drawing a black face card \[=\text{ }E\text{ }=\text{ }3\]

So\[,\text{ }n\left( E \right)\text{ }=\text{ }3\]

Hence, probability of drawing a black face card \[=~n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }3/49\]

\[\left( ii \right)\] Number of queen cards left \[=\text{ }3\]

Event of drawing a black face card \[=\text{ }E\text{ }=\text{ }3\]

So\[,\text{ }n\left( E \right)\text{ }=\text{ }3\]

Hence, probability of drawing a queen card \[=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }3/49\]

 

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