Question

A card is drawn from a pack of 52 cards. Find the probability of drawing a 5 of spade or 8 of hearts.

Answer 1

Hint : These are commonly asked questions in exams. This one is related to a pack of 52 cards. Now we know that there is only one card of spade of 5 and one card of heart of 8 in that pack. So this is our answer. We will add the probabilities of both the conditions to get the answer.

Complete step-by-step answer :
Given is the pack of 52 cards.
So total cards are 52.
Now in that pack there are 13 cards of each suit namely heart, diamond, spade and club.
But in each suit a card from 1 to 10 and then J,Q and K appear once.
Now the probability of drawing a 5 of spades will be $\dfrac{1}{{52}}$ because there is one card to be drawn from one suit and from 52 cards.
Similarly probability of drawing 8 of hearts will be $\dfrac{1}{{52}}$ because there is one card to be drawn from one suit and from 52 cards.
So the probability in total will be,
$= \dfrac{1}{{52}} + \dfrac{1}{{52}}$
So adding this we get,
$= \dfrac{2}{{52}}$
On simplifying we get,
$= \dfrac{1}{{26}}$
Thus we can say,
$P\left( E \right) = \dfrac{1}{{26}}$
This is the correct answer.
So, the correct answer is “$\dfrac{1}{26}$”.

Note : Here note that, we have taken 52 cards in the second case also because there is no condition written for the replacement of cards. If the card drawn first is not replaced then we need to take 51 cards in the second case.
Also note that if instead of a pack we would be asked to take a card from suits only in the question we would have written the condition as 1 from 13 cards only.