Question

The king, queen and jack of clubs are removed from a pack of $52$ playing cards. One card is selected at random, find the probability that the card is a $10$ of hearts.

Answer 1

Step 1: Finding the favorable and total number of outcomes

In a pack of cards, there are $52$ cards.

On removal of king, queen and jack of clubs the total cards will be $52-3=49$.

The pack of cards contain $13$ cards of each suit clubs, spades, hearts and diamonds.

There is $1$, $10$ of hearts card in a pack.

Step 2: Finding the probability that the drawn card is a $10$ of hearts

The formula for the probability is expressed as,

$Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

Substitute the number of favorable outcomes as $1$ and the total number of outcomes as $49$.

$\therefore P\left(a10ofheartscard\right)=\frac{1}{49}$

Hence, the probability of selecting a $10$ of hearts card from a pack of $52$ cards from which a king, queen and jack of clubs is removed is $\frac{1}{49}$.