one card is drawn from a well shuffled deck of 52 cards. Calculate the probability that the cards will (a) be an ace and (b) not be an ace??
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Well-shuffling ensures equally likely outcomes.
(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
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