Question

A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting:

$(i)$ a king of red colour $(ii)$ a face card $(iii)$ the queen of diamonds.

Answer 1

Hint: Apply the basic method of finding probability,

Probability$ = \dfrac{{{\text{No}}{\text{. of favourable outcomes}}}}{{{\text{No}}{\text{. of possible outcomes}}}}$. In this case, a card is drawn from $52$ cards. So, no. of possible outcomes will always be $52$.

Complete Step-by-Step solution:

A card is to be drawn from a well shuffled pack of $52$ cards. This can be done in $52$ different ways.

So, the total no. of possible outcomes will be $52$ in every case while calculating the probability.

We’ll apply Probability $ = \dfrac{{{\text{No}}{\text{. of favourable outcomes}}}}{{{\text{No}}{\text{. of possible outcomes}}}}$.

$(i)$ In this case, we have to draw a king of red colour. As we know that out of $52$ cards in the deck, $26$ is of red colour. And out of those $26$ red coloured cards, $2$ are kings. So, no. of favourable outcomes is $2$. Therefore the required probability is:

Probability $ = \dfrac{2}{{52}} = \dfrac{1}{{26}}$.

Thus, the probability of drawing a king of red colour is $\dfrac{1}{{26}}$.

$(ii)$ In this case, we have to draw a face card. In a deck of $52$ cards, the cards are divided into $4$ suits. Each suit contains $13$ cards and out of these, $3$ are face cards. Thus, the deck contains a total of $12$ face cards. So, no. of favourable outcomes is $12$. Therefore the required probability is:

Probability $ = \dfrac{{12}}{{52}} = \dfrac{3}{{13}}$.

Thus, the probability of drawing a face card is $\dfrac{3}{{13}}$.

$(iii)$ In this case, we have to draw the queen of diamonds. As we know, the deck contains $13$ cards of diamonds suit out of which only $1$ is queen. So, no. of favourable outcomes is $1$. Therefore the required probability is:

Probability $ = \dfrac{1}{{52}}$.

Thus, the probability of drawing the queen of diamonds is $\dfrac{1}{{52}}$.

Note: A deck of $52$ cards is divided into $4$ suits. $2$ suits are of red colour and rest $2$ are of black colour. Each suit consists of $13$ cards. Thus, there are $26$ cards of red colour and $26$ cards of black colour. Further, each suit also contains $3$ face cards. Therefore, the deck contains a total of $12$ face cards.