Question

Two coins are tossed simultaneously. What is the probability that the second coin would show a tail given that the first coin has shown a head?
A) 0.50
B) 0.25
C) 0.75
D) 0.125

Answer 1

Hint:
Firstly, write the sample space for the given information.
Then, find the number of elements that satisfy the given question from the sample space.
The ratio of the number of elements satisfying the question to the number of elements in sample space gives the answer.

Complete step by step solution:
It is given that; two coins are tossed simultaneously.
We have to find the probability that the second coin would show a tail given that the first coin has shown heads.
We can write the sample space for the given information as \[S = \left\{ {HH,HT,TH,TT} \right\}\].
Thus, $n\left( S \right) = 4$.
Now, according to the information provided in the question, the head should come first and tail after that.
The favorable condition to that in sample space is HT. So, $n\left( Q \right) = 1$ .
So, the probability that the second coin would show a tail given that first coin has shown head is given by $\dfrac{{n\left( Q \right)}}{{n\left( S \right)}} = \dfrac{1}{4}$ .

Thus, the asked probability is 0.25.

Note:
The number of elements in the sample space of a coin tossed n times is given by the formula ${2^n}$.
Here, \[n = 2\] . So, the number of elements in the sample space of the given question will be 4 because the coin is tossed 2 times and ${2^2} = 4$.