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Probability Ncert Solutions Maths class 11th Maths Class 11th Probability

27. A card is selected from a pack of 52 cards.

(a) How many points are there in the sample space?

(b) Calculate the probability that the card is an ace of spades.

(c) Calculate the probability that the card is (i) an ace (ii) black card.

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alok kumar singh | Contributor-Level 10

4 months ago

27. (a) Since there are 52 cards in the sample space,

n (S) = 52.

So, there are 52 sample points.

(b) In a deck of 52 cards there are 4 ace cards of which only one is of spades.

Hence, if A be an event of getting an ace of spades.

n (A) = 1

So, P (A) = $\frac{n (A)}{n (S)} = \frac{1}{52}$ .

(c) (i) Let B be an event of drawing an ace. As there are 4 ace cards we have,

n (B) = 4

So, P (B) = $\frac{n (B)}{n (S)} = \frac{4}{52} = \frac{1}{13}$ .

(ii) Let D be an event of drawing black cards. Since there are 26 black cards we have,

n (D) = 26.

So, P (D) = $\frac{n (D)}{n (S)} = \frac{26}{52} = \frac{1}{2}$

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$∴ s u m$ of ${| z |}^{2} = {(\frac{1 + \sqrt[]{2}}{2})}^{2} + \frac{1}{4} + {(\frac{1 - \sqrt[]{2}}{2})}^{2} + \frac{1}{4} + 0^{2} + O^{2}$

= $\frac{3}{4} + \frac{\sqrt[]{2}}{2} + \frac{1}{4} + \frac{3}{4} - \frac{\sqrt[]{2}}{2} + \frac{1}{4} = \frac{3}{2} + \frac{1}{2} = 2$

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27. A card is selected from a pack of 52 cards.

(a) How many points are there in the sample space?

(b) Calculate the probability that the card is an ace of spades.

(c) Calculate the probability that the card is (i) an ace (ii) black card.

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27. A card is selected from a pack of 52 cards. (a) How many points are there in the sample space? (b) Calculate the probability that the card is an ace of spades. (c) Calculate the probability that the card is (i) an ace (ii) black card.

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27. A card is selected from a pack of 52 cards.

(a) How many points are there in the sample space?

(b) Calculate the probability that the card is an ace of spades.

(c) Calculate the probability that the card is (i) an ace (ii) black card.