Question

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is:
(A) $\dfrac{1}{2}$
(B) $\dfrac{3}{4}$
(C) $\dfrac{1}{4}$
(D) $\dfrac{2}{3}$

Answer 1

In the given question, we are provided with a coin and a die and we have to calculate the probability so that an odd number appears on the die and the head appears on the coin. So, we will first calculate the probability of individual events and then use the multiplication rule of probability to find the final answer.

Complete step-by-step solution:
So, we have to first find the probability of getting an odd number on die and head on a coin separately.
So, there are a total of six numbers: $1,2,3,4,5,6$ on the die. Out of these six numbers, three numbers: $1,3,5$ are odd.
So, the total number of possibilities for rolling a die is six. Number of favorable outcomes is three.
Therefore, probability of getting an odd number on the die is $\left( {\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}} \right)$
$= \dfrac{3}{6} = \dfrac{1}{2}$
Similarly, while tossing a coin, we have two possibilities: heads or tails.
Number of favorable outcomes is $1$.
Hence, probability of getting a head on the coin is $\left( {\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}} \right)$
$= \dfrac{1}{2}$
Now, we know the multiplication rule of probability for independent events according to which probability for two independent events is the product of probabilities of two separate events. We say two events are independent if the occurrence of one does not change the probability of a second.
So, the probability of getting a head on the coin and an odd number on the die is a product of both the probabilities.
So, $P = \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}$.
So, the option (C) is the correct answer.

Note: In such a problem, one must know the multiplication rule of counting as consequent events are occurring. One must take care while doing the calculations and should recheck them so as to be sure of the final answer. We must know the concepts and definition of independent events to solve the given problem.