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 If A and B are two independent events and P(AUB) =2/5; P(B) = 1/3. Find P(A).
  • a)
     2/9
  • b)
     -1/3
  • c)
    2/10
  • d)
    1/10
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If A and B are two independent events and P(AUB) =2/5; P(B) = 1/3. Fin...
To find the probability of event A, we can use the formula of probability of the union of two events:

P(AUB) = P(A) + P(B) - P(A∩B)

Given that P(AUB) = 2/5 and P(B) = 1/3, we can substitute these values into the formula:

2/5 = P(A) + 1/3 - P(A∩B)

Since A and B are independent events, the probability of their intersection, P(A∩B), is equal to the product of their individual probabilities:

P(A∩B) = P(A) * P(B)

Now we can substitute this into the equation:

2/5 = P(A) + 1/3 - P(A) * P(B)

Since we know that P(B) = 1/3, we can substitute this value as well:

2/5 = P(A) + 1/3 - P(A) * (1/3)

Simplifying the equation, we get:

2/5 = P(A) + 1/3 - P(A)/3

Multiplying both sides of the equation by 15 to eliminate the fractions:

6 = 5P(A) + 5/3 - 5P(A)/3

Now, let's simplify further:

6 = 15P(A) + 5 - 5P(A)

Combining like terms:

6 = 10P(A) + 5

Subtracting 5 from both sides:

1 = 10P(A)

Finally, dividing both sides by 10:

P(A) = 1/10

Therefore, the correct answer is option 'D' (1/10).
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If A and B are two independent events and P(AUB) =2/5; P(B) = 1/3. Find P(A).a)2/9b)-1/3c)2/10d)1/10Correct answer is option 'D'. Can you explain this answer?
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