# 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}

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