Question

Find the probability of a card that is selected at random from a pack of cards will be a red honor.

Answer 1

Solve using probability formula:

We know that, probability of an event $\mathbf{=}\mathbf{}\frac{\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{favourable}\mathbf{}\mathbf{outcomes}}{\mathbf{total}\mathbf{}\mathbf{possible}\mathbf{}\mathbf{outcomes}}$

Also, it is known that the total number of cards in a deck $=52$

There are total $8$ red honor cards in a deck of cards namely ace, king, queen, and jack of hearts and ace, king, queen, and jack of diamonds.

i.e., the total number of red honor cards $=8$

Therefore the probability of drawing a red honor card is,

Probability of drawing a red honor card $=\frac{\mathrm{number}\mathrm{of}\mathrm{red}\mathrm{honor}\mathrm{cards}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{cards}\mathrm{in}\mathrm{a}\mathrm{deck}}$

$\Rightarrow$ Probability of drawing a red honor card $=\frac{8}{52}$

$\Rightarrow$ Probability of drawing a red honor card $=\frac{2}{13}$

Hence, the probability of a card that is selected at random from a pack of cards will be a red honor is $\frac{2}{13}$.