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Question

Two cards are drawn one by one from a pack of cards. The probability of getting first card an ace and second a coloured one is (before drawing second card first card is not placed again in the pack)


A

126

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B

552

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C

5221

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D

413

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Solution

The correct option is C

5221


Find the required probability:

Step 1: Find the probability of drawing an ace card

In a pack of 52 cards there are 4 aces

Let Abe the event of drawing an ace

pA=452

There are in total 16 coloured cards in a pack of 52 cards. They are 4 aces, 4 kings, 4 queens and 4 jacks.

After drawing the first card as an ace we are not placing it back into the deck

Hence, now there are 51 cards out of which 15 are coloured cards.

Step 2: Find the probability of drawing a coloured card

Let B be the the event of drawing an coloured card

We know that pBA=1551 as the probability of event B is calculated given the event A has happened.

A and B are independent events.

Using the formula for conditional probability we get

pBA=pABpA

pAB=pBA×pA

=1551×452

=517×113

pAB=5221

Therefore, the probability of getting first card as an ace ‘and’ a second coloured card is 5221 .

Hence, option (C) is the correct answer.


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