India Site

If A card is drawn at random from a pack of $52$ cards then Find the probability that the card drawn is:(v) neither a heart nor a king (vi) spade or an ace

(v) Total number of heart cards are $13$ and king are $4$ in which king of heart is also included.

Now, the total number of cards that are a heart and a king $=13+3=16$

Thus, the total number of cards that are neither a heart nor a king $=52–16=36$

As We know that, Probability = Number of favorable outcomes/ Total number of outcomes

Therefore, the probability of getting cards neither a heart nor a king $=36/52=9/13$

(vi) Total number of spade cards is $13$

Total number of aces are $4$ in which ace of spade is included in the number of spade cards.

Thus, the total number of cards which are spade or ace $=13+3=16$

As We know that, Probability = Number of favorable outcomes/ Total number of outcomes

Therefore, the probability of getting cards that is spade or an ace $=16/52=4/13$