Question

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting
(i) a red face card.
(ii) neither spade card nor face card
(iii) an ace card.​

Answer 1

$\large\underline{\sf{Solution-}}$

We know that,

$\sf\:Probability \: of \: an \: event =\dfrac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}$

Calculation :-

In a playing card,

• There are 52 cards.

Therefore,

• The total number of possible outcomes = 52

(i) A red face card :

• Number of favourable outcomes i.e. red face cards are 6 out of 52 cards.

Therefore,

• Probability of getting red face card is

$\bf :\longmapsto\:P(getting \: red \: face \: card) = \dfrac{6}{52} = \dfrac{3}{26}$

(ii) Neither spades nor face cards.

In playing cards,

• There are 13 spades and 12 face cards, in which 3 face cards are of spades.

• So, number of spades or face cards = 13 + 9 = 22

• So, number of favourable outcomes, i. e. neither spades nor face card = 52 - 22 = 30

Therefore,

• Probability of getting neither spades nor face cards is

$\rm:\longmapsto\:P(getting\: neither\: spade \: nor \: face\: card) = \dfrac{30}{52} = \dfrac{15}{26}$

(iii) An ace card.

• Number of favourable outcomes i.e. ace cards are 4 out of 52 cards.

Therefore,

• Probability of getting an ace card is

$\bf :\longmapsto\:P(getting \: an\: ace \: card) = \dfrac{4}{52} = \dfrac{1}{13}$

Explore more :-

• The sample space of a random experiment is the collection of all possible outcomes.

• An event associated with a random experiment is a subset of the sample space.

• The probability of any outcome is a number between 0 and 1.

• The probability of sure event is 1.

• The probability of impossible event is 0.

• The probabilities of all the outcomes add up to 1.

• The probability of any event A is the sum of the probabilities of the outcomes in A.

Answer 2

Answer:

(I) 3/26

(ii) 15/26

(iii) 1/13