# A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king.

Given:

A card is drawn at random from a pack of 52 cards.

To do:

We have to find the probability that the card drawn is neither a heart nor a king.

Solution:

A pack of cards contains 52 cards of four suits and two colours red and black.

Each suit has 1 to 13 numbers in which 4 are ace, jack, queen and king.

This implies,

The total number of possible outcomes $n=52$.

Number of cards which are neither a heart nor a king $=52-(13+3)=52-16=36$

Total number of favourable outcomes $=36$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the card drawn is neither a heart nor a king $=\frac{36}{52}$

$=\frac{9}{13}$

The probability that the card drawn is neither a heart nor a king is $\frac{9}{13}$.

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Updated on: 10-Oct-2022

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