probability - One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will (i) be an ace, (ii) not be an ace.

Krishna (last edited 2 years ago) (Expert, Educator @Qalaxia)

Step 1: Understand the given question and find the number of possible outcomes.

In a standard deck, there are 52 cards plus 2 joker cards. There are 4 suits- Spades, Diamonds, Clubs and Hearts. So, there are 13 cards of each suit.

In each suit, there are 9 number cards from 2–10, a Jack, a Queen, a King and an Ace. So, we can say that there are a total of 9*4= 36 number cards; 4 Jacks; 4 Queens; 4 Kings and 4 Ace cards.

The number of possible outcomes = 52 (GIVEN)

Step 2: Calculate the number of fevourable out comes.

There are 4 aces in a deck.

(i) Let E be the event 'the card is an ace.

The number of outcomes favourable to E = 4

(ii) Let F be the event 'card drawn is not an ace.

The number of outcomes favourable to the event F = 52 - 4 = 48

Step 3: Find the probability that the card will be an ace and not be an ace.

Probability P(E)=\frac{number\ of\ fevourable\ out\ comes}{total\ number\ of\ possible\ out\ comes}

Probability of that the card will be an ace P(E) = \frac{4}{52} = \frac{1}{13}

Probability of that the card will not be an ace P(F) = \frac{48}{52} =\frac{12}{13}

We known that complementary events, Here F is the same as 'not E' because there are only two events.

P(F) + P(B) or (P (\bar{F})) = 1

P(F) = 1 - P(B)

P(F) = 1 - \frac{1}{13}= \frac{12}{13}