1.

If P(A) = 2/15, P(B) = 4/15, and P(A ∪ B) = 6/15 Find P(A|B)

**Answer: Option 'C'**

**P(A|B) = P(A ∪ B)/P(B)
P(A|B) = (6/15)/(4/15) = 3/2.**

2.

If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)?

**Answer: Option 'B'**

**P(B|A) = P(A n B)/P(A)
P(A n B) = P(B|A) × P(A)
P(A n B) = 0.2 × 0.18
P(A n B) = 0.36**

3.

Let A and B be independent events with P (A) = 0.2 and P(B) = 0.8. Find P(A/B)?

**Answer: Option 'A'**

**P(A/B) = P (A n B)/P(B)
Here, P (A n B) = 0.16
P(A/B) = 0.16/0.8 = 0.2**

4.

Events A and B are such that P (A) = 1/3, P(B) = 7/6, and P(not A or not B) = 1/4. State whether A and B are independent?

**Answer: Option 'B'**

**P(A) = 1/3, P(B) = 7/6
Also P(A n B) = P
P(A n B) = 1/4
Now P(A) P(B) = 1/3 × 7/6 = 7/18
But P(A n B) = 1/4
Clearly P(A n B) ≠ P(A) × P(B)
Thus, A and B are not independent events**

5.

If A and B are two events such that P (A) = 3/4, P (B) = 1/2 and P (A n B) = 3/8, find P (not A and not B).

**Answer: Option 'B'**

**P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (3/4 + 1/2 - 3/8)
P(not A and not B) = 1 - (7/8)
P(not A and not B) = 1/8.**

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