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

Last updated date: 20th Jun 2024
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Hint: Probability is a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
Experiment: Any phenomenon like rolling a dice, tossing a coin, drawing a card from a well-shuffled deck, etc.
Outcome: The Result of any event; like number appearing on a dice, side of a coin, drawn out card, etc.
Sample Space: The set of all possible outcomes.
Event: Any combination of possible outcomes or the subset of sample space; like getting an even number on rolled dice, getting a head/tail on a flipped coin, drawing out a king/queen/ace of any suit.
Probability Function: A function giving the probability for each outcome.
There are total $52$ cards where Half of the cards are Red and Half are Black i.e. $26$.
Probability $= \dfrac{{Total\,outcomes\,occurred}}{{Total\,No.\,of\,outcomes}}$
“J, Q, K, A” of all the sets are called Honor cards.
There are $8$ Red honor cards are there in total $52$ cards.

Total No. of cards $= \,52$
Total No. of Red cards $= 26$
Total No. of Red honor cards $= 8$
So, a red honor cards can be selected in $8$ ways
So, required probability $= \dfrac{8}{{52}} = \dfrac{2}{{13}}$
So, the probability that a card drawn at random from a deck of $52$ cards is Red honor is$\dfrac{2}{{13}}$.
Note: There an ‘n’ no. of ways to choose from the deck of $52$ cards and then choosing $8$ red honor cards from that $26$ Red cards.
Then probability $= \dfrac{8}{{26}} \times \dfrac{{26}}{{52}}$
$= \dfrac{2}{{13}}$
Here the probability of red honor cards from $26$ cards is $\dfrac{8}{{26}}$.
And probability of Red cards from a deck of $52$ cards is $\dfrac{{26}}{{52}}$.