Answer
Verified
382.9k+ views
Hint: There are 52 cards in a deck. The probability of finding a card can be calculated by dividing the number of cards of the given type by the total number of cards.
Complete step-by-step answer:
Total number of cards (T) = 52
(i) a black king:
In a deck of cards, there are two black kings, one of spade and one of clubs.
\[\therefore \] Probability of finding a black king \[=\dfrac{2}{25}=\dfrac{1}{13}\]
(ii) either a black card or a king:
Total black cards = 13 x 2 = 26
Total kings other than black cards = 2
\[\therefore \] Probability $=\dfrac{2\times 26}{52}=\dfrac{28}{52}=\dfrac{7}{13}$
(iii) a jack, a queen or a king:
Total jacks = 4
Total queens = 4
Total kings = 4
\[\therefore \] Probability $=\dfrac{4+4+4}{52}=\dfrac{12}{52}=\dfrac{3}{13}$
(iv) neither an ace nor a king:
The required cards are all cards other than kings and aces.
$\Rightarrow \left( T \right)-\left( number\ of\ kings+number\ of\ aces \right)$
Number of kings = 4
Number of aces = 4
\[\therefore \] Probability $=\dfrac{\left( T \right)-\left( 4+4 \right)}{52}=\dfrac{52-8}{52}=\dfrac{44}{52}=\dfrac{11}{13}$
(v) a spade or an ace
Number of cards of spades = 13
Aces other than spades = 4 – 1 = 3
\[\therefore \] Probability $=\dfrac{3}{13}$
(vi) neither a red card nor a queen
Required cards are all cards other than red cards and queens.
Red cards = 13 x 2 = 26
Queens other than those included in red cards = 4 – 2 = 2
Therefore, probability $=\dfrac{T-\left( 26+2 \right)}{52}$
$\begin{align}
& =\dfrac{52-28}{52} \\
& =\dfrac{24}{52} \\
& =\dfrac{6}{13} \\
\end{align}$
(vii) other than an ace
Required cards are all cards other than ace.
$\Rightarrow T-\left( number\ of\ aces \right)$
Number of aces = 4
\[\therefore \] Probability $=\dfrac{T-4}{52}=\dfrac{52-4}{52}=\dfrac{48}{52}=\dfrac{12}{13}$
(viii) a ten
Number of tens = 4
\[\therefore \] Probability $=\dfrac{4}{52}=\dfrac{1}{13}$
(ix) a spade
Number of spades = 13
\[\therefore \] Probability $=\dfrac{13}{52}=\dfrac{1}{4}$
(x) a black card
Number of black cards = number of spades + number of clubs
= 13 + 13 = 26
\[\therefore \] Probability $=\dfrac{26}{52}=\dfrac{1}{2}$
(xi) the seven of clubs
There are only one seven clubs in one deck of cards.
\[\therefore \] Probability $=\dfrac{1}{52}$
(xii) a jack
Number of jacks = 4
\[\therefore \] Probability $=\dfrac{4}{52}=\dfrac{1}{13}$
(xiii) the ace of spades
There is only one ace of spades in a deck of cards.
\[\therefore \] Probability $=\dfrac{1}{52}$
(xiv) a queen
Number of queens = 4
\[\therefore \] Probability $=\dfrac{4}{52}=\dfrac{1}{13}$
(xv) a heart
Number of hearts = 13
\[\therefore \] Probability $=\dfrac{13}{52}=\dfrac{1}{4}$
(xvi) a red card
Number of red cards = number of hearts + number of diamonds
= 13 + 13 =26
\[\therefore \] Probability $=\dfrac{26}{52}$
(xvii) neither a king nor a queen
The required cards are all cards except kings and queens.
$\begin{align}
& \Rightarrow T-\left( number\ of\ kings\ +\ number\ of\ queens \right) \\
& \Rightarrow T-\left( 4+4 \right) \\
\end{align}$
\[\therefore \] Probability $=\dfrac{52-8}{52}=\dfrac{44}{52}=\dfrac{11}{13}$
Note: (1) Make sure to not count a card twice like in part (ii) or (v).
(2) Ace is not a face card. Many students make that mistake.
(3) This is the distribution of a deck of playing cards:
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each; i.e. spades, hearts, diamonds and clubs. Cards of spades and clubs are black cards. Cards of hearts and diamonds are red cards. The cards in each suit are ace, king, queen, jack or knaves, 10, 9, 8, 7, 6, 5, 4, 3 and 2.
Complete step-by-step answer:
Total number of cards (T) = 52
(i) a black king:
In a deck of cards, there are two black kings, one of spade and one of clubs.
\[\therefore \] Probability of finding a black king \[=\dfrac{2}{25}=\dfrac{1}{13}\]
(ii) either a black card or a king:
Total black cards = 13 x 2 = 26
Total kings other than black cards = 2
\[\therefore \] Probability $=\dfrac{2\times 26}{52}=\dfrac{28}{52}=\dfrac{7}{13}$
(iii) a jack, a queen or a king:
Total jacks = 4
Total queens = 4
Total kings = 4
\[\therefore \] Probability $=\dfrac{4+4+4}{52}=\dfrac{12}{52}=\dfrac{3}{13}$
(iv) neither an ace nor a king:
The required cards are all cards other than kings and aces.
$\Rightarrow \left( T \right)-\left( number\ of\ kings+number\ of\ aces \right)$
Number of kings = 4
Number of aces = 4
\[\therefore \] Probability $=\dfrac{\left( T \right)-\left( 4+4 \right)}{52}=\dfrac{52-8}{52}=\dfrac{44}{52}=\dfrac{11}{13}$
(v) a spade or an ace
Number of cards of spades = 13
Aces other than spades = 4 – 1 = 3
\[\therefore \] Probability $=\dfrac{3}{13}$
(vi) neither a red card nor a queen
Required cards are all cards other than red cards and queens.
Red cards = 13 x 2 = 26
Queens other than those included in red cards = 4 – 2 = 2
Therefore, probability $=\dfrac{T-\left( 26+2 \right)}{52}$
$\begin{align}
& =\dfrac{52-28}{52} \\
& =\dfrac{24}{52} \\
& =\dfrac{6}{13} \\
\end{align}$
(vii) other than an ace
Required cards are all cards other than ace.
$\Rightarrow T-\left( number\ of\ aces \right)$
Number of aces = 4
\[\therefore \] Probability $=\dfrac{T-4}{52}=\dfrac{52-4}{52}=\dfrac{48}{52}=\dfrac{12}{13}$
(viii) a ten
Number of tens = 4
\[\therefore \] Probability $=\dfrac{4}{52}=\dfrac{1}{13}$
(ix) a spade
Number of spades = 13
\[\therefore \] Probability $=\dfrac{13}{52}=\dfrac{1}{4}$
(x) a black card
Number of black cards = number of spades + number of clubs
= 13 + 13 = 26
\[\therefore \] Probability $=\dfrac{26}{52}=\dfrac{1}{2}$
(xi) the seven of clubs
There are only one seven clubs in one deck of cards.
\[\therefore \] Probability $=\dfrac{1}{52}$
(xii) a jack
Number of jacks = 4
\[\therefore \] Probability $=\dfrac{4}{52}=\dfrac{1}{13}$
(xiii) the ace of spades
There is only one ace of spades in a deck of cards.
\[\therefore \] Probability $=\dfrac{1}{52}$
(xiv) a queen
Number of queens = 4
\[\therefore \] Probability $=\dfrac{4}{52}=\dfrac{1}{13}$
(xv) a heart
Number of hearts = 13
\[\therefore \] Probability $=\dfrac{13}{52}=\dfrac{1}{4}$
(xvi) a red card
Number of red cards = number of hearts + number of diamonds
= 13 + 13 =26
\[\therefore \] Probability $=\dfrac{26}{52}$
(xvii) neither a king nor a queen
The required cards are all cards except kings and queens.
$\begin{align}
& \Rightarrow T-\left( number\ of\ kings\ +\ number\ of\ queens \right) \\
& \Rightarrow T-\left( 4+4 \right) \\
\end{align}$
\[\therefore \] Probability $=\dfrac{52-8}{52}=\dfrac{44}{52}=\dfrac{11}{13}$
Note: (1) Make sure to not count a card twice like in part (ii) or (v).
(2) Ace is not a face card. Many students make that mistake.
(3) This is the distribution of a deck of playing cards:
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each; i.e. spades, hearts, diamonds and clubs. Cards of spades and clubs are black cards. Cards of hearts and diamonds are red cards. The cards in each suit are ace, king, queen, jack or knaves, 10, 9, 8, 7, 6, 5, 4, 3 and 2.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
The states of India which do not have an International class 10 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Name the three parallel ranges of the Himalayas Describe class 9 social science CBSE