Probability Concepts

Probability (getting a green ball) = (4/12) = 1/3

Probability (not getting a green ball) = 1 – Probability (getting a green ball) = 2/3

1. The probability of rolling a 3 on a fair six-sided die is 1/6 because there is one favorable outcome (rolling a 3) out of six possible outcomes (1 through 6).
2. The probability of getting heads on a fair coin is 1/2 because there are two equally likely outcomes (heads or tails).

To find the probability of both events occurring, you multiply the probabilities of each event:

Probability (rolling a 3 and getting heads) = (1/6) * (1/2) = 1/12

Number of favorable outcomes (red marbles) = 10 Total number of possible outcomes (all marbles in the jar) = 30

So, the probability of getting a red marble is:

Probability = 10/30 = 1/3

Number of favorable outcomes (black cards) = 26 Total number of possible outcomes (all cards in the deck) = 52

So, the probability of drawing a black card is:

Probability = 26/52 = 1/2

Probability of event A (P(A)) = 0.6 Probability of event B (P(B)) = 0.7

To find the probability of both events A and B occurring (P(A and B)), you multiply their probabilities:

P(A and B) = P(A) * P(B) = 0.6 * 0.7 = 0.42

So, the probability of both events A and B occurring, given that they are independent, is 0.42.

Number of favorable outcomes (blue marbles) = 4 Total number of possible outcomes (all marbles) = 5 (red) + 4 (blue) + 3 (green) = 12

So, the probability of drawing a blue marble is:

Number of blue marbles / Total number of marbles = 4/12 = 1/3

The probability of drawing a blue marble from the bag is 1/3.

If events A and B are mutually exclusive, it means that they cannot occur at the same time. In this case, to find the probability of either event A or event B occurring, you can simply add their individual probabilities.

Probability of event A (P(A)) = 0.3 Probability of event B (P(B)) = 0.4

To find the probability of either event A or event B occurring (P(A or B)), you add their probabilities:

P(A or B) = P(A) + P(B) = 0.3 + 0.4 = 0.7

So, the probability of either event A or event B occurring is 0.7.

There are two possible ways to get one head and one tail in two coin flips:

1. HT (head-tail)
2. TH (tail-head)

The probability of getting a head (H) or a tail (T) on a single coin flip is both 1/2 since the coin is fair.

calculate the probability of each of the two possibilities

Probability of HT = (1/2) * (1/2) = 1/4

the probability of drawing two red cards is:

(26/52) * (25/51)

There are three even numbers (2, 4, and 6) on a standard six-sided die, and there are a total of six possible outcomes (1, 2, 3, 4, 5, and 6). So, the probability is calculated as:

Number of favorable outcomes (even numbers) / Total number of possible outcomes = 3/6 = 1/2.