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Five cards — the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put a side, what is the probability that the second card picked up is

a). an ace?

b). a queen?

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1 Answer

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Total no. of possible outcomes = 5 {5 cards}

(i) E ⟶ event of getting a good pen.

No. of favourable outcomes = 132 {132 good pens}

P (E) = (No.of favorable outcomes)/(Total no.of possible outcomes)

∴ P(E) = 1/5

(ii) If queen is drawn & put aside,

Total no. of remaining cards = 4

(a) E ⟶ event of getting a queen.

No. of favourable outcomes = 1 {1 ace card}

Total no. of possible outcomes = 4 {4 remaining cards}

P(E) = 1/4

(b) E ⟶ event of getting a good pen.

No. of favourable outcomes = 0 {there is no queen}

P(E) = 0/4=0

∵ E is known as impossible event.

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