Question

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

Answer 1

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.

Complete step-by-step answer:
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 \[\dfrac{{26}}{{52}}\].