*If A and B are any two events, then probability that at least one of them occurs is _________.*
1️⃣ P(A) + P(B) - 2P(A∩B)
2️⃣ P(A) + P(B) - P(A∩B)
3️⃣ P(A) + P(B) + 2P(A∩B)
4️⃣ P(A) + P(B)
Answers
Answered by
2
Answer:
Exactly one of the events of E
A and B is represented by A∩
B
+
A
∩B
hence P(A∩
B
)+P(
A
∩B)={P(A)−P(A∩B)}+{P(B)−P(A∩B)}
=P(A)+P(B)−2P(A∩B)
which is option (A).
⇒P(A∩
B
)+P(
A
∩B)=[P(A)+P(B)−P(A∩B)]−P(A∩B)=P(A∪B)−P(A∩B)
which is option (C).
P(A∩
B
)+P(
A
∩B)=1−P(
A
)+1−P(
B
)−2{1−P(
A
∪
B
)}
=2P(
A
∪
B
)−P(
A
)−P(
B
)={2P(
A
)+2P(
B
)−2P(
A
∩
B
)}−P(
A
)−P(
B
)
=P(
A
)+P(
B
)−2P(
A
∩
B
)
which is option (D).
and P(A∩
B
)+P(
A
∩B)=1−P(
A
∪B)+P(
A
∩B)
∵
A∩
B
=
A
∪B
by demorgan's law P(A∩
B
)=1−P(
A
∪B)
⇒P(A∩
B
)+P(
A
∩B)={1−P(
A
)−P(B)+P(
A
∩B)}+P(
A
∩B)
=P(A)−P(B)+2P(
A
∩B)
for more refer to topper
Similar questions