# 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 ace of spades.

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

Answer

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Hint: In this question we will find the probability by knowing the different types of cards in the pack of cards.

Complete step-by-step answer:

Now, in a pack of 52 cards, there are four different types of cards which are spade, heart, diamond and club. Each has 13 cards each making a total of 52 cards. Out of 52 cards, 26 cards are black and 26 are red in colour. Diamond and heart are red in colour while spade and club are black. Each type has card numbering from 1 to 10 and three face cards over which J, Q, K is written. The card with number 1 is also called an ace. So, there are a total 4 aces and 12 face cards.

Now, to find probability we will apply the formula of probability,

Probability = Number of favourable outcomes / numbers of total outcomes

Now, we will solve (a). When a card is selected from a pack of 52 cards, the number of possible outcomes is 52, i.e. the sample space contains 52 elements. So, there are 52 points in the sample space.

Now, solving (b). Here we have to find the probability that the card is ace of spade. Now, there is only one ace of spade in a pack of 52 cards. So, our favourable outcome = 1 and total number of outcomes = 52.

So, probability that card is an ace of spades = $\dfrac{1}{{52}}$

Now solving (c). Solving (i), there are 4 aces in a pack of 52 cards, each of spade, club, diamond, heart.

So, our favourable outcome = 4.

Probability that the card drawn is an ace = $\dfrac{4}{{52}} = \dfrac{1}{{13}}$.

Solving (ii), there are 26 black cards, so our favourable outcome = 26

Probability that the card drawn is a black card = \[\dfrac{{26}}{{52}} = \dfrac{1}{2}\]

Note: While solving the questions of probability ensure that you read the question properly and give the answer according to the question. Apply a proper formula and check if there is an error in the calculation.

Complete step-by-step answer:

Now, in a pack of 52 cards, there are four different types of cards which are spade, heart, diamond and club. Each has 13 cards each making a total of 52 cards. Out of 52 cards, 26 cards are black and 26 are red in colour. Diamond and heart are red in colour while spade and club are black. Each type has card numbering from 1 to 10 and three face cards over which J, Q, K is written. The card with number 1 is also called an ace. So, there are a total 4 aces and 12 face cards.

Now, to find probability we will apply the formula of probability,

Probability = Number of favourable outcomes / numbers of total outcomes

Now, we will solve (a). When a card is selected from a pack of 52 cards, the number of possible outcomes is 52, i.e. the sample space contains 52 elements. So, there are 52 points in the sample space.

Now, solving (b). Here we have to find the probability that the card is ace of spade. Now, there is only one ace of spade in a pack of 52 cards. So, our favourable outcome = 1 and total number of outcomes = 52.

So, probability that card is an ace of spades = $\dfrac{1}{{52}}$

Now solving (c). Solving (i), there are 4 aces in a pack of 52 cards, each of spade, club, diamond, heart.

So, our favourable outcome = 4.

Probability that the card drawn is an ace = $\dfrac{4}{{52}} = \dfrac{1}{{13}}$.

Solving (ii), there are 26 black cards, so our favourable outcome = 26

Probability that the card drawn is a black card = \[\dfrac{{26}}{{52}} = \dfrac{1}{2}\]

Note: While solving the questions of probability ensure that you read the question properly and give the answer according to the question. Apply a proper formula and check if there is an error in the calculation.

Last updated date: 28th Sep 2023

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