Ex.15.1 Q14 Probability Solution - NCERT Maths Class 10

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Question

One card is drawn from a well-shuffled deck of \(52\) cards. Find the probability of getting

     (i) a king of red colour  (ii) a face card  
     (iii) a red face card (iv) the jack of hearts
     (v) a spade  (vi) the queen of diamonds

 

Text Solution

   

What is known?

One card is drawn from a well-shuffled deck of \(52\) cards.

What is unknown?

The probability of getting

     (i) a king of red colour  (ii) a face card  
     (iii) a red face card (iv) the jack of hearts
     (v) a spade  (vi) the queen of diamonds

Reasoning:

This question can be solved easily by using the formula

Probability of an event \(\begin{align}=\frac{\text{ Number of possible outcomes }}{\text{Total no of favourable outcomes}}\end{align}\)

Steps:

Total number of cards from a well-shuffled deck = \(52\)

No of spade cards= \(13 \)

No of heart cards= \(13\)

No of diamond cards= \(13\)

No of club cards= \(13\)

Total number of kings = \(4\)

Total number of queens= \(4\)

Total number of jack cards = \(4\)

No of face cards = \(12\)

(i) Probability of getting a king of red colour

\[\begin{align} \text{  }&=\frac{\text{Number of red colour king}}{\text{Total no of outcomes}} \\ &=\frac{2}{52}=\frac{1}{26} \end{align}\]

(ii) Probability of getting a face card

\[\begin{align} \text{  } & =\frac{\text{ Number of face cards }}{\text{ Total no of outcomes }} \\ {} & =\frac{12}{52}=\frac{3}{13} \\\end{align}\]

(iii) Probability of getting a red face card

\[\begin{align}&=\frac{\text{ Number of red face cards}}{\text{Total no of outcomes}} \\ &=\frac{6}{52}=\frac{3}{26} \\ \end{align}\]

(iv) Probability of getting the jack of hearts

\[\begin{align}&{ = \frac{{{\text{ Number of jack of hearts}}}}{{{\text{total no of outcomes}}}}}\\{}&{= \frac{1}{{52}}}
\end{align}\]

(v) Probability of getting a spade card

\[\begin{align}&=\frac{\text{ Number of spade cards}}{\text{Total no of outcomes}} \\&=\frac{13}{52}\\&=\frac{1}{4} \\\end{align}\]

 (vi) Probability of getting the queen of diamonds 

\[\begin{align} &= \frac{\text{ Number of possible outcomes }}{\text{ Total no of favourable outcomes}} \\ & =\frac{1}{52} \\ \end{align}\]