Statistics and Probability Determination
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1. For each part, decide whether the blank should be filled in with =, <, or >, and give a short but clear explanation.
a. (probability that the total after rolling 2 fair dice is 9) ___ (probability that the total after rolling 2 fair dice is 10)
b. (number of ways to split 10 basketball players into 2 teams of 5) ___ (10 5)
c. probability of observing heads twice in a row before observing tails followed immediately by Heads, in a long sequence of flips of a fair coin) ___ 1/2
2. A codeword is a sequence of at least one (and possibly all) of the usual 26 letters A, B, C, D, E....Z with repetitions not allowed. For example, COURSE is a codeword, but STATISTICS is not a codeword. Order matters (e.g. COURSE is not the same as SOURCE). A codeword is chosen randomly, with all codewords equally likely. Show that the probability that the random codeword uses all 26 letters is very close to 1/e.
3. You are invited to attend 6 weddings next year, independently with all months of the year equally likely. What is the probability that no two weddings are in the same month?
See attachment for better formula representation.
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Solution Summary
This solution identifies the correct symbol representation for the statements, shows the probability of a random codeword being 1/e and also determines the probability of no two weddings occur in the same month. All steps are shown with brief explanations.
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Q1:
Part a)
We have following possibilities of getting a sum of 9 after rolling 2 fair dice
3,6 4,5 5,4 6,3
Hence
P(x=9)=4/36
We have following possibilities of getting a sum of 10 after rolling 2 fair dice
4,6 5,5 6,4
Hence
P(x=10)=3/36
Thus P(X=9) >= P(X=10)
b)
The best way is to think like we select one team of 5 members from given 10 player. The second team is automatically ...
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