Question

Three coins are tossed. If one of them shows a tail, then the probability that all three coins show a tail is
1) 1/7
2) 1/8
3) 2/7
4) 1/6

Answer 1

Hint:Find the set of possibilities included in both the conditions and substitute the possibilities in the general equation. Hence we can find the probability value. It might be challenging to predict many things with complete certainty. By using probability, we are only able to anticipate the likelihood, or probability, of an event occurring.

Formula Used:
The general form is $P(A/B)=P(A\cap B)/P(B)$

Complete step by step Solution:
Assume that A is the occurrence of all three coins showing a tail, and B is the occurrence of one coin showing a tail.
$\mathrm{A}=\{\mathrm{TTT}\}$
$\mathrm{B}=\{\mathrm{HHT}, \mathrm{HTH}, \mathrm{THH}, \mathrm{HTT}, \mathrm{THT}, \mathrm{TTH}, \mathrm{TTT}\}$
$\mathrm{A} \cap \mathrm{B}=\{\mathrm{TTT}\}$
A set called an intersection B has components that are found in both sets A and B. The intersection of sets A and B is shown by the $\cap$symbol, which is interpreted as "A intersection B" and written as$A \cap B$. The set of components shared by all sets is the intersection of two or more sets.
Therefore, the required probability $=P(A / B)$
$P(A/B)=P(A\cap B)/P(B)$
$P(A / B)=P(A \cap B) / P(B)=1 / 7$

Hence, the correct option is 1.

Note:Note that there are numerous alternative probability interpretations, probability theory provides a clear understanding of the idea by defining it in terms of a collection of axioms or hypotheses. These theories aid in forming the probability in terms of possibility space, allowing for a measure with values ranging from 0 to 1. To a group of potential outcomes in the sample space, this is referred to as the probability measure.