Question

Five cards- ten, jack, queen, king and an ace of diamonds are shuffled face downwards. One card is picked at random.
(i) What is the probability that the card is a queen?
(ii) If a king is drawn first and put aside, what is the probability that the second card picked up is the (1) ace (2) king.

Answer 1

Hint:Here, we will use the concept of probability to find the required probabilities of the given favorable events. The probability of any event E is given as:
$P\left( E \right)=\dfrac{\text{favourable number of outcomes}}{\text{total number of outcomes}}$

Complete step-by-step answer:
Probability is concerned about the numerical description of how likely an event is to occur or how likely it is that a proposition is true.
The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates the certainity. The higher the probability of the event, the more likely it is that the event will occur.
Here, we have been given five cards that are – ten, jack, queen, king and an ace of diamonds.
(i) In the first part, we have to find the probability of drawing a queen.
Since, we know that, here total number of cards is = 5
And, number of queens is = 1
So, probability that the card drawn is a queen is given as:
$P=\dfrac{\text{number of queens}}{\text{total number of cards}}=\dfrac{1}{5}$
(ii) Similarly in the second case when a king is drawn and kept aside, the total number of cards becomes 4.
(1) So, the probability that the second card is an ace is:
$P=\dfrac{\text{number of aces }}{\text{total number of cards}}=\dfrac{1}{4}$
(2) And, the probability of drawing a king is given as:
$P=\dfrac{\text{number of kings}}{\text{total number of cards}}=\dfrac{0}{4}=0$
Hence, answer for part (i) $\dfrac{1}{5}$ and answers for part (ii) (1) $\dfrac{1}{4}$ and (2) $0$.

Note: Students should note here that we can directly say that the probability of drawing a king in the second case is 0 because the king has already been kept aside.A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%