Q: Which formula correctly represents the multiplicative rule of probability for independent events A and B?

$$P(A \cap B) = P(A) \times P(B)$$

Question 1

Which of the following best describes the additive rule of probability?

Accepted Answer

The probability that either of two mutually exclusive events occurs is the sum of their individual probabilities.

Question 2

A die is tossed once. What is the probability that the result is either a 2 or a 5?

Accepted Answer

$$\frac{2}{6}$$

Question 3

If two coins are tossed, what is the probability that both land heads?

Accepted Answer

$$\frac{1}{4}$$

Question 4

Which formula correctly represents the multiplicative rule of probability for independent events A and B?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 5

A student randomly guesses on five multiple-choice questions, each with five options. What is the probability that the student gets exactly three correct answers?

Accepted Answer

$$P_3$$ = \frac{5!}{(5-3)!3!} \left(\frac{1}{5}\$$right)^3$$ \left(\frac{4}{5}\$$right)^2$$

Question 6

Given the set of all possible outcomes when rolling two dice (as shown in the image), what is the probability that the sum is 4?

Accepted Answer

$$\frac{3}{36}$$

Question 7

If you know that the sum of two dice is 4, what is the probability that both dice show 2?

Accepted Answer

$$\frac{1}{3}$$

Question 8

Which of the following is the correct formula for the binomial probability of getting exactly X successes in n trials?

Accepted Answer

$$P(X) = \frac{n!}{(n-X)!X!} p^X q$$^{n-X}$$

Question 9

A coin is tossed three times. What is the probability of getting exactly two heads?

Accepted Answer

$$\frac{3}{8}$$

Question 10

A family has two children. If you know one is a boy, what is the probability that both are boys?

Accepted Answer

$$\frac{1}{3}$$

Question 11

Which of the following statements about independent events is correct?

Accepted Answer

The probability of both events occurring is the product of their individual probabilities.

Question 12

If $$p is $$the probability of success and $$q is $$the probability of failure in a binomial experiment, what is the relationship between $$p$$ and $$q$$?

Accepted Answer

$$p + q = 1$$

Question 13

A fair coin is flipped four times. What is the probability of getting exactly three heads?

Accepted Answer

$$\frac{1}{4} = \frac{4}{16}$$

Question 14

Which of the following is an example of a conditional probability?

Accepted Answer

The probability of drawing a red card from a deck, given that the card is a heart.

Question 15

If a genetic cross produces offspring with a 3:1 ratio of dominant to recessive phenotypes, what is the probability of randomly selecting two offspring and both being recessive?

Accepted Answer

$$\frac{1}{16}$$

Probability Rules and Binomial Distribution in Transmission Genetics

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