Life Expectancy. The probability that a randomly selected 40-year-female will li

Question

Life Expectancy. The probability that a randomly selected 40-year-female will live to be 41 years old is 0.99855 according to the National Vital Statistics Report, Vol. 56. No 9 a) What is the probability that three randomly selected 40-year-old females will live to be 41 years old? b) What is the probability that at least one of four randomly selected 40-year-old female will not live to be 41 years old? 3. Effectiveness of Vaccine. A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographical region, 25% of the people get vaccinated. If a person is selected at random, find the probability that he or she will contract the disease. (Hint: This is a total probability problem] 4. Planting Tulips. A bag of 35 tulip bulbs purchased from a nursery contains 14 red tulip bulbs, 9 yellow tulip bulbs, and 12 purple tulip bulbs. Two tulip bulbs are drawn without replacements a) What is the probability that two randomly selected tulip bulbs are both red? b) What is the probability that first bulb selected is yellow and the second is red? c) What is the probability that the first bulb selected is red and the second is purple? d) What is the probability that at least one tulip is purple? 5. Children. A family has five children. If this family has exactly two boys, how many different! birth and gender orders are possible?

Explanation / Answer

2)a) probability =(0.99855)3 =0.995656

b)probability that at least one of 4 will not live to be 41 =1-P(all live to be 41) =1-(0.99855)4 =0.005787

3)P(contract disease) =P(vaccinated and cotract  disease+not vaccinated and cotract  disease)

=0.25*0.1+(1-0.25)*0.5 =0.4

4)

a)P(both are red) =(14/35)*(13/34)=0.1529

b) P(first yellow and second red) =(9/35)*(14/34)=0.1059

c) P(1st red and second purple) =(14/35)*(12/34)=0.1412

d)P(at least one tulip) =1-P(none are tulip) =1-(1-12/35)*(1-12/34)=0.5748

5) from multinomial distribution ; number of ways to arranging them =5!/(2!3!) =10

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