Given that the events A and B are such that PA-1-2- PB-p- PA- B-3-5- Find p if A and B are- I mutually exclusive ii independent-

P(A)=1/2,P(B)=pP(AUB)=3/5i) Mutually exclusive #160;P(A ∩ B)=0P(AUB)=P(A)+P(B) P(A ∩ B)3/5=1/2+p 0p=1/10ii)Independent events #160;P(A ∩ B)=P(A) ...

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Standard XII

Mathematics

Probability Distribution

Given that th...

Question

Given that the events A and B are such that $P (A) = \frac{1}{2}, P (B) = p, P (A \cup B) = \frac{3}{5}$ . Find p if A and B are. (I) mutually exclusive (ii) independent.

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Solution

P(A)=1/2,P(B)=p
P(AUB)=3/5
i) Mutually exclusive P(A $\cap$ B)=0
P(AUB)=P(A)+P(B)-P(A $\cap$ B)
3/5=1/2+p-0
p=1/10
ii)Independent events P(A $\cap$ B)=P(A)*P(B)=p/2
P(AUB)=P(A)+P(B)-P(A $\cap$ B)
3/5=1/2+p-p/2
p=1/5

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Given that the events A and B are such that P(A)=12,P(B)=p,P(A∪B)=35. Find p if A and B are. (I) mutually exclusive (ii) independent.

P(A)=1/2,P(B)=pP(AUB)=3/5i) Mutually exclusive P(A∩B)=0P(AUB)=P(A)+P(B)-P(A∩B)3/5=1/2+p-0p=1/10ii)Independent events P(A∩B)=P(A)*P(B)=p/2P(AUB)=P(A)+P(B)-P(A∩B)3/5=1/2+p-p/2p=1/5

Given that the events A and B are such that $P (A) = \frac{1}{2}, P (B) = p, P (A \cup B) = \frac{3}{5}$ . Find p if A and B are. (I) mutually exclusive (ii) independent.

P(A)=1/2,P(B)=p
P(AUB)=3/5
i) Mutually exclusive P(A $\cap$ B)=0
P(AUB)=P(A)+P(B)-P(A $\cap$ B)
3/5=1/2+p-0
p=1/10
ii)Independent events P(A $\cap$ B)=P(A)*P(B)=p/2
P(AUB)=P(A)+P(B)-P(A $\cap$ B)
3/5=1/2+p-p/2
p=1/5