Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. what is the probability that they belong to different suits? - Mathematics

The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. what is the probability that they belong to different suits?

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Solution

Having removed 12 face cards, the remaining 40 cards include 10 cards in each suit. 
∴ Chance of drawing a card in the first draw = \[\frac{^{40}{}{C}_1}{^{40}{}{C}_1} = 1\]

Having drawn 1 card, there remain 39 cards of which 30 are of suits different from the drawn card.
∴ Chance of drawing a card of different suit in the second draw =  \[\frac{^{30}{}{C}_1}{^{39}{}{C}_1} = \frac{30}{39}\]

Having drawn two cards, there remain 38 cards of which 20 are of suits different from the drawn cards.

∴ Chance of drawing a card of in the third draw =\[\frac{^{20}{}{C}_1}{^{38}{}{C}_1} = \frac{20}{38} = \frac{10}{19}\]

Having drawn three cards, there remain 37 cards of which 10 are of suits different from the drawn cards.
∴ Chance of drawing a card in the fourth draw =\[\frac{^{10}{}{C}_1}{^{37}{}{C}_1} = \frac{10}{37}\]

Hence, all the events being dependent, the required probability =\[1 \times \frac{30}{39} \times \frac{10}{19} \times \frac{10}{37} = \frac{1000}{9139}\]

 

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 18 | Page 46
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