Homework #4-Chap10 (20pts for turned in on time) 1. (4pts) We have learned 5 pro
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Homework #4-Chap10 (20pts for turned in on time) 1. (4pts) We have learned 5 probability rules in Chapter 10, which of the following rule is NOT correct? A. For any event A, its probability P(A) has to be within 0 and 1 B. The probability of the whole sample space is 1 C. If A and B are two disjoint events, then P (A and B) P(A)P(B). D. For any event A, P (A doesn't occur) 1-P(A) 2. (4pts) A coin has two faces (head and tail). If two coins are tossed, and the number of heads (X) are recorded, what is the sample space of variable X? A. Head and Tail B. (Head, Head), (Head, Tail), Tail, Head), and (Tail, Tail) C. 0,1, 2 D. 0, 1, 2,3 3. (10pts)The human blood types can be one of A, B, AB and O, which is our sample space (A the possible outcomes of the blood types). The probability for blood types in United States are: Blood T Probabili AB 0,42 0.11 0.44 a. (Spts)What is probability of randomly selected person blood type to be AB in United States? b. (5pts)Maria has type B blood, so she can receive blood transfusions from people with type B or type O. What is the probability that a randomly selected person in U.S. can donate blood to Maria? 4. (10pts)The distribution of blood type in Ireland differs from U.S. and is given below Blood T AB 0.03 Probabili Choose one person from Ireland and choose one person from U.S. can be considered independent. If one person is randomly selected from U.S. and another person is randomly selected from Ireland, find the probability of the following event (You will need the information from question 5 as well for this question). 0.35 0.10 0.52 a. (Spts)(US person blood type is A and Ireland person blood type is B) b. (5pts)KUS person blood type is not A and Ireland person blood type is B)Explanation / Answer
1. Option c is incorrect. Since two disjoint events are always mutually exclusive/dependent since if one occurs the other cannot occur. P(A and B)= P(A)P(B) is true for independent events. Options a,b.d are correct.
2.X is the number of heads shown on the toss of 2 coins. It can be 0,1,2. Example( Head on both coins, Heads on any one, Heads on none) We are not concerned with Tails. So our sample space is option C. 0,1,2
3. a) The total probability of a sample space is 1. So the probability that a randomly selected person has AB group = 1-0.42-0.11-0.44= 0.03
b) Maria can recieve blood from group b or group o. So required probability that a randomly selected person can donate blood to her is 0.11+0.44=0.55
4. a) Since the events are independent we have REQUIRED PROBABILITY= P(A from US)*P(B ireland) = 0.42*0.10= 0.042
b) P(US not A)*P(B ireland) = (1-0.42)*0.1= 0.058
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