Q: A fair six-sided die is rolled twice. What is the probability that at least one of the rolls results in a 5? Use the complement rule.

$$1 - (\frac{5}{6} \times \frac{5}{6}) = 0.3056$$

Q: If you flip a fair coin twice, what is the probability that it will come up heads at least once?

$$1 - (0.5 \times 0.5) = 0.75$$

Q: If you roll two fair six-sided dice, what is the probability that both dice show a 5?

$$\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$$

Q: If you flip a fair coin four times, what is the probability of getting exactly two heads?

$$\binom{4}{2} \times (0.5)^2$ \times (0.5)^2$ = 6 \times 0.0625 = 0.375$$

Q: A geneticist is studying a trait controlled by two independent genes. What is the probability that an offspring will inherit the dominant allele for both genes if each parent is heterozygous for both genes?

$$\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$$

Q: If you roll two fair six-sided dice, what is the probability that neither die shows a 5?

$$\frac{5}{6} \times \frac{5}{6} = 0.6944$$

Question 1

If you flip a fair coin three times, what is the probability that it will come up heads all three times? Use the multiplication rule for independent events.

Accepted Answer

$$0.125$$

Question 2

A fair six-sided die is rolled twice. What is the probability that at least one of the rolls results in a 5? Use the complement rule.

Accepted Answer

$$1 - (\frac{5}{6} 	imes \frac{5}{6}) = 0.3056$$

Question 3

In a dihybrid cross between two heterozygous pea plants (RrGg x RrGg), what is the probability of obtaining an offspring with the genotype rrgg?

Accepted Answer

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

Question 4

If you flip a fair coin twice, what is the probability that it will come up heads at least once?

Accepted Answer

$$1 - (0.5 	imes 0.5) = 0.75$$

Question 5

Which of the following best describes the role of probability in genetics?

Accepted Answer

It predicts the likelihood of different genetic outcomes, not certainties.

Question 6

If you roll two fair six-sided dice, what is the probability that both dice show a 5?

Accepted Answer

$$\frac{1}{6} 	imes \frac{1}{6} = \frac{1}{36}$$

Question 7

A couple are both heterozygous for a gene (Aa x Aa). What is the probability that their child will be homozygous recessive (aa)?

Accepted Answer

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

Question 8

If you flip a fair coin four times, what is the probability of getting exactly two heads?

Accepted Answer

$$\binom{4}{2} 	imes (0.5)^2$ 	imes (0.5)^2$ = 6 	imes 0.0625 = 0.375$$

Question 9

In a genetic cross, the probability of inheriting allele A from one parent is 0.5. What is the probability of inheriting allele A from both parents?

Accepted Answer

$$0.5 	imes 0.5 = 0.25$$

Question 10

If you roll a fair six-sided die, what is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{2}{6} = \frac{1}{3}$$

Question 11

A geneticist is studying a trait controlled by two independent genes. What is the probability that an offspring will inherit the dominant allele for both genes if each parent is heterozygous for both genes?

Accepted Answer

$$\frac{3}{4} 	imes \frac{3}{4} = \frac{9}{16}$$

Question 12

If you flip a fair coin five times, what is the probability of getting heads every time?

Accepted Answer

$$(0.5)^5 = 0.03125$

Question 13

In a dihybrid cross (RrGg x RrGg), what is the probability of an offspring being heterozygous for both genes (RrGg)?

Accepted Answer

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

Question 14

If you roll two fair six-sided dice, what is the probability that neither die shows a 5?

Accepted Answer

$$\frac{5}{6} 	imes \frac{5}{6} = 0.6944$$

Question 15

A couple are both heterozygous for two genes (RrGg x RrGg). What is the probability that their child will be homozygous recessive for both genes (rrgg)?

Accepted Answer

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

Question 16

If you flip a fair coin twice, what is the probability that it will come up tails both times?

Accepted Answer

$$0.5 	imes 0.5 = 0.25$$

Probability in Genetics: Foundations and Applications

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