Question

Problem #1 (8 points) Suppose you have gone bowling with an excellent player who bowls a strike (ie when they hit all of the pins) 73% of the time. By the fourth frame, this person realizes that they can clincha first place in a local tournament by bowling 3 consecutive strikes. What is the likelihood of this happening! Problem #2: Part a (8 points): Mammograms are a very widely used screening tool for breast cancer. However, according to one study (Note: this is made up) false positives on mammograms occur at a rate of about 8%. That is, about 8% of patients without cancer still have positive findings on mammograms (accoring to this one - pretend-study). Suppose a healthy patient i.e. someone who turns out not have cancer) gets a manumogram every year. What is the probability of that patient encountering at least one false positive after 4 years of testing? Note: Again, the 8% quoted earlier is purely fictional and used for purposes of this problem. Part b (3 points): Real world application: When interpreting statistics, it is often important to try to interpret statistical scenarios without necessarily have expertise in the particular area. Try to do so bere: Think about or research the consequences of a false positive test for breast cancer? Why is a false positive test problematie? Problem #3 (6 points) A recent census allowed each person to choose from a long list of races. That is, in the eyes of the Census Bureau, you helong to whatever race you say you belong to If we choose a resident of the United States at random. The census gives these probabilities: Hispanic Not-Hispanic Asian 0.000 0.056 African-American 0.014 0.11 White 0.160 0.591 Other 0.032 0.037 Let A be the event that a randomly chosen American identifies themselves as Non-Hispanic Let B be the event that the person identifies as white, Let C be the event that a person identifies as Hispanic. Let D be the event that a person identifies as African-American a) The third row on the chart sums to 0.751. We will refer to this row as 'B'. Explain in words what is meant by the symbol: P(B). Explain in words what is meant by the symbol P(B). b) Describe what is meant by C in words and then give the value of P(C) c) Express the person chosen is African-American and Hispanic in terms of these probability symbols using A and/or Band/or C and/or D.

It is understood that in number 4, the blood types do not add up to 1.0 and that is fine.

Answer 1

Answer: 1. Likelihood of this event =P(Bowling 3 Consecutive strikes) +(0.13) +0.389 the 4 years 2. a) Poquite pootability is equal to - poolability that the patient doemot get false positive report in As pCfelse positive report) 28.1.10.08 Hence, plnot getting false positive report the sun geon) =(1-8.03) *= 0.71639296 PC getting at least one false positive report) 1-0.71639296 0.28360704 5) Since plat least one false positive report)=0.28 ~0.28>00s, so the probability is quite high which will make the healthy patient worry. 1 As he doesn't have the problems. The false positive is problemotic as it can make a healthy parson sick mentally 3a PCS30-451 is the probability that a randomly chosen resident of the USA is White. O PCBC): 1-0.75170.249 is the probability that a randomly chosen resident of the USA is not white. Scanned with

b) c in words: A rondomly chosen person is non. Hispanic. 11+0.891 +0.037 -0.794. c) D show that the person is African-America e shows that person is Hispanic: So, one shows that the person choosens is African American & Hispanic: 1 4 Giver, Blood HP- А в AB о Regional Probability 0.44 0.09.0.05 .446 Rh factor Rh positive Phregative Regional probabiling -087 ??' a) sample space for Rs (0,12:3;44. b) PCall 4 donors are Rh negative) te P(Ph negative)-1-0-87 20:13 pCall Hp Ph regalive) - (0:13) * 0.00028561 Op Coondoroiy selected individual is Rh negative and for blood type o op (en negative) wple) Regione To -0.1370:46= 0.0598 cs Scained with Can Scanner

Dolnone of the donors have blood type B) • C-PCB))" =(1-0.09% (0.9D 0.686 e) plat least one of the donos have AB) = 1- P(none have AB) ar-Cl-oros)" cs Scanned with O: 18551) CamScanner