Q: A plant breeder crosses two heterozygous plants (Gg x Gg) and collects pods with 8 seeds each. What is the probability of finding a pod with exactly 1 green seed (green is recessive, $$q = 0.25$$)?

$$P = 8 \times (0.75)^7$ \times (0.25)^1$

Question 1

Which of the following best describes the product rule in probability theory as applied to Mendelian genetics?

Accepted Answer

It is used to calculate the probability of independent events occurring together by multiplying their individual probabilities.

Question 2

A couple has three children. What is the probability that they will have exactly two boys and one girl, assuming the probability of having a boy or girl is equal?

Accepted Answer

$$P = \frac{3!}{2!1!} (\frac{1}{2})^2$ (\frac{1}{2})^1$ = 3 	imes \frac{1}{8} = \frac{3}{8}$$

Question 3

In a cross between two heterozygous yellow-seeded pea plants (Gg x Gg), what is the probability that a yellow-seeded offspring is heterozygous?

Accepted Answer

$$\frac{2}{3}$$

Question 4

Which formula correctly represents the binomial probability of obtaining exactly $$k$$ successes in $$n$$ independent trials, each with probability $$p of $$success?

Accepted Answer

$$P = \frac{n!}{k!(n-k)!} p^k (1-p$$)^{n-k}$$

Question 5

If you flip a fair coin 4 times, what is the probability of getting exactly 3 heads?

Accepted Answer

$$P = \frac{4!}{3!1!} (\frac{1}{2})^3$ (\frac{1}{2})^1$ = 4 	imes \frac{1}{16} = \frac{1}{4}$$

Question 6

A pod contains 6 seeds, each of which can be yellow (probability $$p = 0.75) or $$green ($$q = 0.25). $$What is the probability that exactly 4 seeds are yellow and 2 are green?

Accepted Answer

$$P = \frac{6!}{4!2!} (0.75)^4$ (0.25)^2$

Question 7

Which of the following statements about the sum rule in probability is correct?

Accepted Answer

It is used to calculate the probability of mutually exclusive events by adding their individual probabilities.

Question 8

In a chi-square test, which formula is used to calculate the chi-square statistic?

Accepted Answer

$$\$$chi^2$$ = \sum \frac{(O - E)^2$}{E}$$

Question 9

A geneticist observes 5474 round and 1850 wrinkled seeds in an F2 generation, where the expected numbers are 5493 round and 1831 wrinkled. What is the chi-square value for this experiment?

Accepted Answer

$$\$$chi^2$$ = \frac{(5474-5493)^2$}{5493} + \frac{(1850-1831)^2$}{1831} = 0.066 + 0.197 = 0.263$$

Question 10

What is the degrees of freedom (df) for a chi-square test with three possible phenotypic classes?

Accepted Answer

$$df = 2$$

Question 11

If the probability of a result occurring by chance (p-value) is less than 0.05 in a chi-square test, what does this indicate?

Accepted Answer

The observed results are significantly different from the expected results.

Question 12

A plant breeder crosses two heterozygous plants (Gg x Gg) and collects pods with 8 seeds each. What is the probability of finding a pod with exactly 1 green seed (green is recessive, $$q = 0.25$$)?

Accepted Answer

$$P = 8 	imes (0.75)^7$ 	imes (0.25)^1$

Question 13

Which of the following best describes a normal distribution in the context of Mendelian inheritance experiments?

Accepted Answer

It is a bell-shaped curve representing the distribution of experimental outcomes around the mean.

Question 14

In a binomial probability distribution with $$n = 10$$ and $$p = 0.5$$, what is the most likely number of successes?

Accepted Answer

5

Question 15

Which of the following is NOT a requirement for using the chi-square test in genetics?

Accepted Answer

The sample size must be greater than 100.

Question 16

A true-breeding red, early-blooming cherry tree is crossed with a yellow, late-blooming tree. The F1 is selfed, and the F2 shows the following: 501 red/early, 155 red/late, 163 yellow/early, 49 yellow/late. What is the degrees of freedom for a chi-square test of independent assortment?

Accepted Answer

3

Question 17

Which of the following best describes conditional probability in genetics?

Accepted Answer

It is the probability of an event given that another event has already occurred.

Question 18

If you observe a chi-square value that corresponds to a p-value greater than 0.05, what should you conclude?

Accepted Answer

There is no significant difference between observed and expected values; fail to reject the null hypothesis.

Probability Theory and Statistical Analysis in Mendelian Genetics

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