Probability

A fair coin is tossed three times. The probability of getting exactly two heads is

1. 1/8
2. 3/8
3. 1/2
4. 5/8

If X is a random variable with mean E(X) and variance Var(X), then Var(X) is equal to

1. E(X²) - [E(X)]²
2. E(X)² - E(X²)
3. E(X²) + [E(X)]²
4. E(X) + E(X²)

The mean of a discrete random variable X is calculated using

1. E(X) = ΣxP(x)
2. E(X) = Σx/P(x)
3. E(X) = ΣP(x)
4. E(X) = Σx²P(x)

For a discrete random variable X, the sum of all possible probabilities is

1. 0
2. 1
3. Greater than 1
4. Negative

A random variable X has the following probability distribution: X: 0, 1, 2 with P(X): 0.2, 0.5, 0.3. The value of P(X = 1) is

1. 0.2
2. 0.3
3. 0.5
4. 1

According to Bayes' Theorem, the probability of event A when event B has occurred is given by

1. P(A|B) = P(A) + P(B)
2. P(A|B) = [P(B|A)P(A)] / P(B)
3. P(A|B) = P(A)P(B)
4. P(A|B) = P(A)/P(B|A)

If A and B are independent events, then which relation is true?

1. P(A|B) = P(A)
2. P(A|B) = 0
3. P(A|B) = P(B)
4. P(A|B) = 1

A bag contains 3 red balls and 2 blue balls. If one ball is drawn at random, the probability of drawing a red ball is

1. 2/5
2. 3/5
3. 1/5
4. 3/2

If P(A) = 1/2 and P(B|A) = 1/3, then P(A ∩ B) is

1. 1/6
2. 1/3
3. 1/2
4. 2/3

If P(A) = 0.6, P(B) = 0.5, and P(A ∩ B) = 0.3, then P(A|B) is

1. 0.5
2. 0.6
3. 0.8
4. 0.3

If P(A) = 0.3 and P(B) = 0.5, and A and B are independent, then P(A ∩ B) is

1. 0.8
2. 0.15
3. 0.2
4. 0.35

If events A and B are independent, then

1. P(A ∩ B) = P(A) + P(B)
2. P(A ∩ B) = P(A) × P(B)
3. P(A ∩ B) = 0
4. P(A) = P(B)

If P(A) = 0.4, P(B) = 0.5, and A and B are mutually exclusive, then P(A ∪ B) equals

1. 0.2
2. 0.9
3. 1.0
4. 0.1

If two events A and B are mutually exclusive, then

1. P(A ∩ B) = 1
2. P(A ∩ B) = 0
3. P(A ∪ B) = 0
4. P(A) = P(B)

If P(A) = 0.65, then the probability of the complement of A is

1. 0.35
2. 0.65
3. 1.65
4. 0