Q) While shuffling a pack of 52 cards, one card was accidently dropped. Find the probability that the dropped card
(i) is not a face card.
(ii) is a black king.

PYQ: Q 25 – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans:

(ii) Probability to get a non – face card:

[Note: To calculate probability of not getting a face card, let’s first calculate the probability to get a face card and subtract from 1]

Since there are total 52 cards in a pack, and if 1 cards is dropped then it can be anyone of these 52 cards

∴ Total chances = 52

Since there are 12 face cards in a pack of cards,

∴ Total number of favourable chances = 12

Next, we know that the probability = favourable chances / total chances

By substituting the values from above steps, we get

Probability of dropped card being a face card = 12 / 52 = 3 /13

Next, we know that the Probability of NOT occurring an event = 1 – Probability of occurring an event

∴ Probability of dropped card NOT being a face card = 1 – Probability of dropped card being a face card

= 1 – 3 / 13 = 10 / 13

Therefore, the Probability of dropped card NOT being a face card is 10 / 13.

(ii) Probability to get a black king

Again, since there are total 52 cards in a pack, and if 1 cards is dropped then it can be anyone of these 52 cards

∴ Total chances = 52

Since there is only two black kings (Spade and Club) in a pack of cards

∴ Total number of favourable chances for dropped card being a black king = 2

Next, we know that the probability = favourable chances / total chances

By substituting the values from above steps, we get

Probability of dropped card being a black king = 2 / 52 = 1 / 26

Therefore, the Probability of dropped card being a black king is 1 / 26.

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