Question

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.

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Answer 1

Answer:

I) 4/52 = 1/13

ll) 48/52 = 12/13

Answer 2

Answer:

GIVEN :-

• One card is drawn from a well-shuffled deck of 52 cards.
• Well-shuffling ensures equally likely outcomes.

TO FIND :-

Calculate the probability that the card will

(i) be an ace,

(ii) not be an ace.

FORMULAE :-

$P(E) = \frac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes}$

SOLUTION :-

➡️(i) Card drawn is an ace

There are 4 aces in a deck.

Let E be the event ‘the card is an ace’.

The number of outcomes favourable to E = n(E) = 4

The number of possible outcomes = Total number of cards = n(S) = 52

Therefore, P(E) = n(E)/n(S) = 4/52 = 1/13

➡️(ii) Card drawn is not an ace

Let F be the event ‘card drawn is not an ace’.

The number of outcomes favourable to the event F = n(F) = 52 – 4 = 48

Therefore, P(F) = n(F)/n(S) = 48/52 = 12/13