Q. 255.0( 1 Vote )
Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are:
i. p1p2
ii. (1–p1) p2
iii. 1–(1–p1)(1–p2)
iv. p1+p2 = 2p1p2
Answer :
If the events are said to be independent, if the occurrence or non occurrence of one does not affect the probability of the occurrence or non occurrence of other.
i. p1p2
p1p2=P(A)P(B)
Both events A and B will occur
ii. (1–p1) p2
(1–p1) p2=[1–P(A)]P(B)
Event A does not occur but event B occur.
iii. 1–(1–p1)(1–p2)
1–(1–p1)(1–p2)=[1–(1–P(A))(1–P(B))]
At least one of the event will occur
iv. p1+p2 = 2p1p2
p1+p2 = 2p1p2
P(A)+P(B)=2P(A)P(B)
P(A)+P(B)–2P(A)P(B)=0
P(A)–P(A)P(B)+P(B)–P(A)P(B)=0
P(A)[1–P(B)]+P(B)[1–P(A)]=0
Exactly one of A and B occurs
Rate this question :
Probability of occurrence of an event | Quiz Time45 mins
Probability of occurrence of an event45 mins
If A and B are two independent events such that P(A’ ∩ B) = 2/15 and P(A ∩ B’) = 1/6 then find P(A) and P(B).
Mathematics - Board PapersState True or False for the statements in the Exercise.
If A and B are two independent events then P(A and B) = P(A).P(B)
Mathematics - ExemplarState True or False for the statements in the Exercise.
If A and B are mutually exclusive events, then they will be independent also.
Mathematics - ExemplarState True or False for the statements in the Exercise.
If A and B are independent, then
P (exactly one of A, B occurs) = P(A)P(B′)+P(B) P(A′)
Mathematics - ExemplarState True or False for the statements in the Exercise.
If A and B are independent events, then P(A′ ∪ B) = 1 – P (A) P(B′)
Mathematics - ExemplarState True or False for the statements in the Exercise.
Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.
Mathematics - ExemplarProve that if E and F are independent events, then the events E and F are also independent.
Mathematics - Board Papers