Find the probability of describing a single event for the given condition.
James speaks 70% truth and Williams speaks 90% truth.
A.
43/60
B.
33/40
C.
37/50
D.
33/50
Answers
Step-by-step explanation:
Consider the following events,
A
1
: A speaks truth
A
2
: B speaks truth
Then, P(A
1
)=
100
60
=
5
3
,P(A
2
)=
100
70
=
10
7
For the required event,either both of them should speak the truth or both of them should tell a lie.
Thus, the required probability is
P(A
1
∩A
2
)∪(
A
1
∩
A
2
)=P(A
1
∩A
2
)+P(
A
1
∩A
2
)
=P(A
1
)P(A
2
)+P(
A
1
)(
A
2
)
=
5
3
×
10
7
+(1−
5
3
)(1−
10
7
)=0.54
Answer:
The probability of describing a single event for the given condition= 33/50
Step-by-step explanation:
What is Probability?
Probability is any situation which is likely that it will take place. Also how many outcomes can be possible.
In the given question
Given:
P(James speaks truth)= 70%
= 70/100
= 7/10
P(William speaks truth)= 90%
= 90/100
= 9/10
To find:
Probability of them describing a single event?
Solution:
The formula would be:
P(both say the same thing)= P(both speaks the truth)+ P(both lies)
=P(James speaks truth)×(William speaks truth)+ P(James lies)×P(William lies)
= 7/10×9/10+ (1-7/10)(since both are lying)×
(1-9/10)
= 7/10×9/10+3/10×1/10
= 63/100+ 3/100
= 66/100
= 33/50
Therefore, The probability of describing a single event for the given condition= 33/50
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