Question

find the probability of pulling a card As given below from a deck of 52 cards
a a black card
b number more than 5
c a red card and a queen
d a picture card​

Answer 1

Solution :

A 52 card deck consists of :

→ 13 ranks , each containing 4 suites

> 26 black cards

> 26 red cards

> 13 spades ( Black cards )

> 13 clubs ( Black cards )

> 13 diamonds ( Red Cards )

> 13 hearts ( Red Cards )

4 Jacks, 4 kings and 4 queens ; ( 4 different suites )

Coming to the question :

(a) Probability of getting a black card :

> [ 26/52 ]

> 1/2 .

(b) A number more than 5

> This may be 6, 7, 8, 9 and 10, each having 4 suits .

Number of favorable cases :

> 20

Required probability :

> ( 4/20 ) = 1/5 .

(c) A red card and a queen :

The number of favorable cases :

> ( No of red cards ) ∪ ( No of queens ) - ( No of red cards ) ∩ ( No of queens )

> 26 + 4 - 1

> 29 cards

Required probability becomes 29/52 .

(d) A picture card :

The picture cards are always the jack, king and queen cards

No of picture cards :

> 12

Thus, the required probability is 12/52 or 3/13 .

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Answer :

(a) 1/2

(b) 1/5

(c) 29/52

(d) 3/13

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Answer 2

$\large\underline\blue{\bold{Given \:  Question :-  }}$

Find the probability of pulling a card as given below from a deck of 52 cards :-

a) a black card

b) number more than 5

c) a red card and a queen

d) a picture card

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$\huge{AηsωeR} ✍$

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☆ Basic concept on drawing a card:

• In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣.
• Each suit contains an ace (A), king (K), queen (Q), jack or knaves (J), 10, 9, 8, 7, 6, 5, 4, 3, and 2.
• King, Queen, and Jack (or Knaves) are called the face cards. In the deck of 52 playing cards, there are 12 face cards.

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☆ What is probability?

• Probability shows how likely an event will happen.
• The probability of an event E is defined as P(E) = Number of favourable outcomes of E/ total number of possible outcomes of E.

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How to Find the Probability Step by Step

You can use the following steps to calculate the probability:

Step 1: Identify the number of favourable events.

Step 2: Find the total number of results that can occur.

Step 3: Divide the number of favourable events by the total number of possible outcomes.

Formula

P(E) = n(E) /n(S).

• n(E) = Number of favourable outcomes of E.
• n(S) = total number of possible outcomes of E.

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$\bf \:\large \red{AηsωeR : a.} ✍$

☆ There are 26 black cards in pack of 52 cards.

∴ Total number of possible outcomes = 26

$\sf\implies \: \: P (black \: card) = \: \dfrac{ \cancel{26}}{ \cancel{52}} = \dfrac{1}{2}$

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$\bf \:\large \red{AηsωeR : b} ✍$

☆ We, know number greater than 5 in playing cards are 6, 7, 8, 9 and 10 and there are 4 cards of each number.

∴ Total number of possible outcomes = 5 × 4 = 20

$\sf\implies \:P (card \: having \: number \: > 5) =\dfrac{ \cancel{20} \: \: ^5}{ \cancel{52} \: \: ^{13}} = \dfrac{5}{13}$

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$\bf \:\large \red{AηsωeR : c} ✍$

☆ We know, there are 26 red cards in playing cards and 4 queens ( 2 of red color and 2 of black color) in playing card. Here we have to pick red card and queen, so it means its card of red queen

∴ Total number of possible outcomes = 2

$\sf\implies \:P (red \: queen) = \: \dfrac{ \cancel{2} \: \: ^1}{ \cancel{52} \: \: ^{26}} \: = \dfrac{1}{26}$

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$\bf \:\large \red{AηsωeR : d} ✍$

☆ We know, In playing cards, picture cards are Jack, Queen and King, So, there are 4 Jacks, 4 Queens and 4 Kings.

∴ Total number of possible outcomes = 12

$\sf\implies \:P (picture \: card) = \: \dfrac{ \cancel{12} \: \: ^3}{ \cancel{52} \: \: ^{13}} = \dfrac{3}{13}$

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