1. A human gene carries a certain disease from the mother to the child with a probability rate of 57%. That is, there is a 57% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another. Find the probability that all three of the children get the disease from their mother. Round to the nearest thousandth.
2. Gestation Period versus Weight: The following data represent the birth weights (in grams) of babies born in 2013, along with period of gestation.

Period of Gestation

Birth Weight (grams)	Preterm	Term	Postterm	Total
Less than 1000	27096	179	26	27301
1000-1999	78690	10502	1063	90255
2000-2999	221778	661729	38665	922172
3000-3999	119161	2317287	160354	2596802
4000-4999	7390	2757733	24583	307661
Over 5000	220	4019	398	4637
Total	454335	3269449	225044	3948828

• What is the probability that a randomly selected baby born in 2013 was postterm?
• What is the probability that a randomly selected baby born in 2013 weighed 3000-3999 grams?
• What is the probability that a randomly selected baby born in 2013 weighed 3000-3999 grams and was postterm?
• What is the probability that a randomly selected baby born in 2013 weighed 3000-3999 grams or was postterm?
• What is the probability that a randomly selected baby born in 2013 weighed less than 1000 grams and was postterm? Is this event impossible?
• What is the probability that a randomly selected baby born in 2013 weighed 3000-3999 grams, given the baby was postterm?
• Are the event "postterm baby" and "weighs 3000-3999" independent? Explain?

3. For the following questions, considertherollingof adie twicesample space(put a box around your final answer):

• If a die is rolled twice, find the probability that the sum is4.
• If a die is rolled twice, find the probability that the sum is7or the 1^strollis a 3.
• If a die is rolled twice, find the probability that the sum is7giventhat the 1^stroll is a4
• If a die is rolled twice, find the probability that the sum is6giventhat the 2^stroll is a3
• When a die is rolled twice, are the event "sum is 10" and "1^stroll is a 2" disjoint?