Question

A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant. To estimate the probability that a seed from the new plant will germinate, a random sample of 3000 seeds was planted in warm, moist soil. Of these seeds, 2470 germinated.

a. Use relative frequencies to estimate the probability that a seed will germinate. What is your estimate?
b. Use relative frequencies to estimate the probability that a seed will not germinate. What is your estimate?
c. Either a seed germinates or it does not. What is the sample space in this problem? Do the probabilities assigned to the sample space add up to 1? Should they add up to 1? Explain.

1. Yes, because they cover the entire sample space.
2. Yes, because they do not cover the entire sample space.
3. No, because they cover the entire sample space.
d. No, because they do not cover the entire sample space.

d. Are the outcomes in the sample space of part (c) equally likely?

Answer 1

a. The estimate of the probability that a seed will germinate is:

82% (0.82)

b. The estimate of the probability that a seed will not germinate is:

18% (0.18)

c. The sample space is 2.

1. Yes, because they cover the entire sample space. The probabilities assigned to the sample space add up to 1 (0.82 +0.18).

They should always add up to one. Probability summed cannot exceed 1.

Explanation:

a) Data and Calculations:

Sample = 3,000 seeds

Germinated seeds = 2,470

Non-germinated seeds = 530 (3,000 - 2,470)

Probability of a seed germinating = 2,470/3,000 = 82% approx.

Therefore, the probability of a seed not germinating = 18% (100 - 82) or (530/3,000)