Math 2050 Assignment 1 Due Date: 09/22/17 2. A health study tracked a group of p
ID: 3304183 • Letter: M
Question
Math 2050 Assignment 1 Due Date: 09/22/17 2. A health study tracked a group of person for tive years. At the beginning of the study, 20% were classified as heavy smokers, 30% as light smokers, and 50% as nonsmokers. Results of the study showed that light smokers were twice as likely as nonsmokers to die during the five-year study, but only half as likely as heavy smokers. A randomly selected paricipant from the study died during the five-year pcriod. Calculate the probability that the participant was a heavy smoker 1. 2. What is the sample space for tossing a fair coin four times? 3. Consider the experiment of tossing two tair coins. The event A: fobserve exactly one head), and the event B: (observe at least one head!. Calculate the probability of A and the probability bB Consider the die-toss experimen. Detine the following events: A: (Toss an even numbert and B: Toss à number less than or equal to 3 4. a. What are the clements inAvB for this experiment? b. What are the elements in A B fur this experiment? c. Calculate PLA B) and PiA B) assuming the die is lair. Consider the experiment of tossing two fair coins. The event A: (observe exactly one headj, and the event B: johserve at least one head. Find P(A), P(B) 5. PAn R) PIA B), and INB A). 6. Consider the experittient of tossing a fair die aud kt A lobserve an even number) B: (observe a number less than 5). Are events A and B arc independent? 7. For two events, A and B, P(A)-04 and P(B)-02 a. If A and B are indcpendent, find MAr B), PA B) and PA B) b. If A and B are dependent, with PIA jB)-0.6, find PIA nB) and P(B A) 8. Find the curnulative distribution function of the random variable X, where f(0) 1/16, ftly-1:4, fi21-3/8, t(31/4, and f(4):1/16.Explanation / Answer
2. If H - head, T- tail then sample space (collection of all possible outcomes) will be
S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}
3. Sample space for tossing two coin
S= {HH, HT, TH, TT}
A = {exactly one head} = {HT, TH}
B = {atleast one head} ={ HH, HT, TH}
Probability of A = n(A)/ n(S) = 2/4 = 1/2 = 0.5
Probability of B = n(B)/n(S) = 3/4 = 0.75