Question

1. In a survey of U.S. adults with a sample size of 2004, 345 said Franklin Roosevelt was the best president since World War II. TwoTwo U.S. Two adults are selected at random from this sample without replacement. Complete parts​ (a) through​ (d).

​(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.

​(b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II.

​(c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II.

2. The probability that a person in the United States has type B​+ blood is 12%. 4 unrelated people in the United States are selected at random. Complete parts​ (a) through​ (d).

(a) Find the probability that all five have type B​+ blood.

​(b) Find the probability that none of the five have type B​+ blood.

​(c) Find the probability that at least one of the five has type B​+ blood.

​3. A study found that 39% of the assisted reproductive technology​ (ART) cycles resulted in pregnancies. ​Twenty-five percent of the ART pregnancies resulted in multiple births.

​(a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth.

​(b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.

​(c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple​ birth? Explain.

Answer 1

1. In a survey of U.S. adults with a sample size of 2004, 345 said Franklin Roosevelt was the best president since World War II. TwoTwo U.S. Two adults are selected at random from this sample without replacement. Complete parts​ (a) through​ (d).

​(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.

Answer)

Probability is given by favorable/total

Total = 2004

Favorable = adults say franklin roosevelt was the best president = 345

P(first) = 345/2004

P(second) = 344/2003 (as first one is already considered so we are now left with 344 who says franlin was the best president and total left = 2004 - 1 )

P(both) = (345/2004)*(344/2003) = 0.02956642879

​(b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II.

Answer)

P(first ) = (2004-345)/2004 = 1659/2004

P(second) = (1658/2003)

P(both) = (1659/2004)*(1658/2003) = 0.68525505155

​(c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II.

Answer)

For at least 1, we have two cases

First case = 1 says franklin roosevelt was the best president

Second case = both says franklin was the best president = 0.02956642879 (calculated in part a)

First case

P(first one who says franklin was the best president) = 345/2004

P(second one who does not say ) = 1659/2003

P(one says and another one doesnt) = (345/2004)*(1659/2003)

Total probability = first case + second case = 0.17215568861