Xi PLEi] 0.1 PfE%] = 0.2 Y2 4. What is the probability that in a group of 10 peo
ID: 3040837 • Letter: X
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Xi PLEi] 0.1 PfE%] = 0.2 Y2 4. What is the probability that in a group of 10 people, every birthday is in a different month? 5. Angela's father and mother went on a picnic in a park with 10 other friends of theirs. They found a round table in that park and sat down. What is the probability that Angela's parents do not sit next to each other? a. b. What is the probability that her parents sit next to each other with her father sitting to the right of her mother? 6. The probability that a bit is transmitted in error in a certain transmission medium is 0.15. Assume that we use the medium to transmit a message of10 bits and that the outcome of each bit is independent of that of other bits (a) What is the probability that exactly 2 errors occur in the message? (b) What is the probability that at most 2 errors occur in the message? 7. Consider the structure shown below. Switches S, and S, are in series, and the pair is in parallel with a parallel arrangement of switches S, and S,. Their reliability functions are R (O, R,(), R,(C)and R,(0), respectively. The structure interconnects nodes A and B. What is the reliability function of the composite system in terms of R,0), R,(0, R,()and R,() if the switches fail independently? S,Explanation / Answer
4. Here' the stepwise solution to the answer:
Number you and your friends from 1 to 10, where you are #1. The probability that #2's birth month is different from your own is 9/12. The probability that #3's birth month is different from your own and #2 is then 8/12. Keep iterating this, then the probability you all have distinct birth months can be solved by multiplying those probabilities (as all birth months must be distinct to span all 12 months):
= (9/12)*(8/12)*(7/12)*(6/12)*(5/12)*(4/12)*(3/12)*(2/12)*(1/12) = 9!/12^9
= 4.07*10^-8
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