A recent article in the Journal of Urban Chicken Farmers reported the fraction of chickens that experience severe, moderate, or minor side effects from a new diet are 0.07, 0.15, and 0.78, respectively. Assuming that chickens respond independently, if 18 chickens were tested on the new diet, what is the: 3. Probability that 2,4, and 12 chickens will suffer severe, moderate, or minor side effects, respectively? Probability that no chickens will suffer severe side effects? Mean number of chickens that will suffer severe side effects? Variance in the number of chickens that will suffer severe side effects? Conditional mean of the number of chickens that suffer severe side effects given that 17 suffer minor side effects. a. b. C. d. e.
Percentage
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Multiplication rule for independent events:
If two events A and B are independent then the multiplication rule state that:
a.
Find the probability that 2, 4 and 12 chickens will suffer severe, moderate or minor side effects:
Let X be the number of chicken that experience severe side effects, Y be the number of chicken that experience moderate side effects and Z be the number of chicken that experience minor side effects. The probability that the chicken will experience severe side effects is 0.07, the probability that chicken will experience moderate side effects is 0.15 and the probability that chicken will experience minor side effects is 0.78. Assume that there are 18 chickens tested and each the chickens were responding independently. Here the event X follows binomial distribution with n=18 and p=0.07, Y follows binomial distribution with n=18 and p=0.15 and Z follows binomial distribution with n=18 and p=0.78. Then probability that 2, 4 and 12 chickens will suffer severe, moderate or minor side effects using multiplication rule is given below:
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