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Mathematics · Probability · NCERT Examples

Example 4

A complete, independently verified solution for NCERT Example 4.

Mathematics · Chapter 14 · NCERT Examples

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NCERT Example

Example 4

playing cards · ace · complement

One card is drawn from a well-shuffled deck of 52 cards. Find the probability that it will (i) be an ace and (ii) not be an ace.

Solution

Board-exam working:

A deck has 52 cards and 4 aces.

(i) Number of favourable outcomes for drawing an ace = 4.

P(ace)=452=113P(\text{ace})=\frac4{52}=\frac1{13}

(ii) Number of cards that are not aces:

52−4=4852-4=48
P(not an ace)=4852=1213P(\text{not an ace})=\frac{48}{52}=\frac{12}{13}

Check using complementary events:

1−P(ace)=1−113=12131-P(\text{ace})=1-\frac1{13}=\frac{12}{13}

Final answer

(i) 113(ii) 1213\boxed{\text{(i) }\frac1{13}\qquad\text{(ii) }\frac{12}{13}}