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

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Vedantu Content Team · Accepted Answer

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 $$\dfrac{{26}}{{52}}$$.

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

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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.

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