Probabilities

If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.3, what is the probability of both events A and B occurring if they are independent?

• 0.12

• 0.25

• 0.1

• 0.7

If the probability of event A occurring is 0.6 and the probability of event B occurring given that event A has already occurred is 0.4, what is the probability of both events A and B occurring if they are dependent?

• 0.6 + 0.4 = 1.0

• 0.6 / 0.4 = 1.5

• 0.6 - 0.4 = 0.2

• 0.6 * 0.4 = 0.24

In a deck of 52 cards, two cards are drawn successively without replacement. What is the probability that both cards are aces?

What is the probability of flipping a fair coin three times and getting at least two heads?

A box contains 4 defective and 6 non-defective bulbs. If two bulbs are selected at random with replacement, what is the probability that both bulbs are non-defective?

• 0.36

• 0.25

• 0.64

• 0.50

A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a heart and then drawing a spade if the first card is not replaced?

• 1/16

• 1/32

• 1/8

• 1/26

A bag contains 7 green and 5 yellow balls. If three balls are drawn at random without replacement, what is the probability that two balls are green and one is yellow?

• 7/12 * 6/11 * 5/10 = 105/220

• 7/12 * 5/11 * 4/10 = 70/220

• 7/12 * 6/11 * 5/10 = 210/440

• 7/12 * 5/11 * 4/10 = 140/440

What is the formula to calculate the probability of three independent events A, B and C all occurring?

• P(A and B and C) = P(A) * P(B) * P(C)

• P(A and B and C) = P(A) + P(B) + P(C)

• P(A and B and C) = P(A) - P(B) - P(C)

• P(A and B and C) = P(A) / P(B) / P(C)

If the probability of event A occurring is 0.5 and the probability of event B occurring given that event A has already occurred is 0.3, what is the probability of both events A and B occurring if they are dependent?

• 0.5 + 0.3 = 0.8

• 0.5 / 0.3 = 1.67

• 0.5 - 0.3 = 0.2

• 0.5 * 0.3 = 0.15

A bag contains 3 red, 2 blue and 4 green balls. If two balls are drawn at random without replacement, what is the probability that both balls are green?

• 4/9 * 3/8 = 12/72

• 3/9 * 2/8 = 6/72

• 4/9 * 3/8 = 1/6

• 3/9 * 2/8 = 1/12