# Ex.15.1 Q15 Probability Solution - NCERT Maths Class 10

## Question

Five cards the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is

(a) an ace?

(b) a queen?

## Text Solution

**What is known?**

Five cards Sthe ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards and one card is then picked up randomly.

**What is unknown?**

(i)The probability of getting the queen

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

**Reasoning:**

This question can be solved easily by using the formula

Probability of an event

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

**Steps:**

Total no of cards = \(5\)

No of queen cards = \(1\)

(i) Probability that the card is the queen

\[\begin{align} &= \frac{ \begin{Bmatrix} \text{ Number of} \\ \text{possible} \\ \text{ outcomes} \end{Bmatrix}}{\begin{Bmatrix}\text { Total no of} \\ \text{favorable} \\ \text{outcomes} \end{Bmatrix}} \\ &=\frac{1}{5} \end{align}\]

(ii) If the queen is drawn and put aside, then four cards are left the ten, jack, king and ace of diamonds

(a) Probability that the card an ace

\[\begin{align} &= \frac{ \begin{Bmatrix} \text{ Number of} \\ \text{possible} \\ \text{ outcomes} \end{Bmatrix}}{\begin{Bmatrix}\text { Total no of} \\ \text{favorable} \\ \text{outcomes} \end{Bmatrix}} \\ &=\frac{1}{4} \end{align}\]

(b) Probability that the card is the queen

\[\begin{align} &= \frac{ \begin{Bmatrix} \text{ Number of} \\ \text{possible} \\ \text{ outcomes} \end{Bmatrix}}{\begin{Bmatrix}\text { Total no of} \\ \text{favorable} \\ \text{outcomes} \end{Bmatrix}} \\ & =\frac{0}{4} \\ &=0 \end{align}\]