10. Agriculture: Cotton. 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, 2,430 germinated.

(a) Use relative frequencies to estimate the probability that a seed will germinate. What is your estimate?

Solution: The relative frequency is

Therefore, our estimate of the probability that a seed will germinate is 0.81.

(b) Use relative frequencies to estimate the probability that a seed will not germinate. What is your estimate?

Solution: The relative frequency that a seed will not germinate is

Therefore, our estimate of the probability that a seed will not germinate is 0.19.

(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.

Solution: The sample space in this problem is the set of all possible outcomes of numbers of seeds that germinated, which is {0, 1, 2, … , 2999, 3000}. Each outcome has a probability of, and then they add up to 1, which what should happen, because the sample space accounts for all the possible events.



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