Answer
(a) The probability of the event that all three coins show the same face is 0.25, as there are two favorable outcomes $(HHH;TTT)$ out of the sample set:
$P(A)=\frac{2}{8}=0.25$
(b) The probability of the event that at least two coins are tails is 0.5, as there are four favorable outcomes $(TTT;HTT;THT;TTH)$ out of the sample set:
$P(B)=\frac{4}{8}=0.5$
Work Step by Step
The sample set is
$S=${$HHH;HHT;HTH;HTT;TTT;THH;THT;TTH$}, therefore the total number of outcomes is 8.
The probalitity of an event can be calculated as:
$P(A)=\frac{\text{favorable outcomes out of the sample set}}{\text{total number of possible outcomes}}$
This means, that the probability of the event that all three coins show the same face is 0.25, as there are two favorable outcomes $(HHH;TTT)$ out of the sample set:
$P(A)=\frac{2}{8}=0.25$
The probability of the event that at least two coins are tails is 0.5, as there are four favorable outcomes $(TTT;HTT;THT;TTH)$ out of the sample set:
$P(B)=\frac{4}{8}=0.5$
