Rabbits like to eat the cauliflowers in Mimi\'s garden. There are 10 cauliflower

Question

Rabbits like to eat the cauliflowers in Mimi's garden. There are 10 cauliflowers in her garden which will be ready to harvest in about 10 days. Based on her experience, the probability of a cauliflower being eaten by the rabbits before harvest is 0.40. 10. Let X be the number of cauliflowers that Mimi harvests (that is, the number of cauliflowers not eaten by rabbits). As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? (a) Find the probability that Mimi harvests at least 8 of the 10 cauliflowers. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit. (b)

Explanation / Answer

(a) Here the number of trials n is 10 cauliflowers.

Here the probability of failure, i.e the carrot not being harvested or being eaten by a rabbit before the harvest is given as 0.4. So q = 0.4

Therefore the probability of success ,p, = 1 - q = 1 - 0.4 = 0.6

(b) P(Mini harvests at least 8 cauliflowers) = P(8) + P(9) + P(10)

Binomial Probability = nCx * (p)x * (q)n-x, where n = number of trials and x is the number of successes and

nCx = n! / [(n-x)!*x!]

P(8) = 10C8 * (0.6)8 * (0.4)2 = 10!/[(10-2)!8!] * (0.6)8 * (0.4)2 = 45 * (0.6)8 * (0.4)2 =0.12093

P(9) = 10C9 * (0.6)9 * (0.4)1 = 10!/[(10-1)!9!] * (0.6)9 * (0.4)1 = 10 * (0.6)9 * (0.4)1 = 0.04031

P(10) = 10C10 * (0.6)9 * (0.4)0 = 10!/[(10-10)!10!] * (0.6)10 * (0.4)0 = 1 * (0.6)10 * (0.4)0 = 0.00605

Therefore the required probability = 0.12093 + 0.04031 + 0.00605 = 0.16729

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