Two coins are tossed simultaneously. Give example of mutually exclusive?
Answers
Answer:
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Step-by-step explanation:
When two coins are tossed, sample space S is given by {HH,HT,TH,TT} and therefore, n(S)=4.
Let A denote the event that both head appear that is {HH} and n(A)=1, therefore, probability of both head appear is:
P(A)=
n(S)
n(A)
=
4
1
Let B denote the event that both tail appear that is {TT} and n(B)=1, therefore, probability of both tail appear is:
P(B)=
n(S)
n(B)
=
4
1
Intersection of A and B is the common elements between A and B which is none, thus, n(A∩B)=0 and
P(A∩B)=
n(S)
n(A∩B)
=
4
0
=0
Therefore, the events are mutually exclusive.
The probability of either both head or both tail occur is P(A∪B) and we know that for mutually exclusive event, P(A∪B)=P(A)+P(B) that is:
P(A∪B)=P(A)+P(B)=
4
1
+
4
1
=
4
2
=
2
1
Hence, probability that either both heads or both tails occur is
2
1
.