Question

The probability that the drawn card from a pack of 52 cards is neither an ace nor a spade is .
a.9/13
b.35/52
c.10/13
d.19/26​

Answer 1

Answer

a. 9/13

Explanation

No. Of aces in deck of cards = 4

No. of spades n deck of cards = 13

There is once ace of spades, so we will take that card in common.

Total number of cards = 4 + 13 - 1 = 16

thus probability = 1 - 16/52

= 52 -16 / 52

= 36 / 52

= 9 / 13

Answer 2

Given:

Number of cards in a pack of cards = 52

To find:

the probability of the card neither being an ace or spade

Solution:

The total number of cards = 52

The number of aces in a pack of cards = 4

The number of spades in a pack of cards = 13

The total number of aces and spades =

As one of the spades is an ace so one card will be in common therefore the total number of cards will be one less than the sum of spades and aces.

= 4 + 13 - 1

= 16

The total number of cards in the pack that will neither be an ace or a spade

= 52 - 16

= 36

The probability of  a card in the pack neither being an ace or a spade

= Cards in the pack that are neither ace nor spade / total number of cards

= $\frac{36}{52}$

=$\frac{9}{13}$

Therefore, the probability that the drawn card from a pack of 52 cards is neither an ace nor a spade is 9/13.