# Ex.15.1 Q14 Probability Solution - NCERT Maths Class 10

## 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

This question can be solved easily by using the formula

**Reasoning:**

Probability of an event

\[=\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} }\]

**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

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