Calculate the modeled probability in each case. Assume coins and dice are distin

Question

Calculate the modeled probability in each case. Assume coins and dice are distinguishable and fair. All answers should be exact (use fractions rather than decimal approximations). (a) n (S) = 35, n (E) = 20. Assume that the outcomes are equally likely. P (E) = Check Clear (b) 4 coins are tossed: E The result is exactly one head. P (E) = Check Clear (c) A die is thrown: E The result is at most 4. P (E) = Check Clear (d) A pair of distinguishable dice are thrown and the sum of the numbers facing up is noted: E The result is equal to 1. P (E) = Check Clear It is found that the Moon is in the seventh house 72% of the time whereas the moon is in the Seventh House at the same time that Jupiter aligns with Mars 10% of the time. Further, either Jupiter aligns with Mars or the Moon is in the Seventh House (or both) 80% of the time. (a) What percentage of time is Jupiter aligns with Mars? Answer: Check Clear (b) What percentage of time is Jupiter does not align with Mars? Answer: Check Clear (c) What percentage of time is neither Jupiter aligns with Mars nor is the Moon in the Seventh House? Answer: Check Clear

Explanation / Answer

5) a) P(E) = 20/35 = 0.57143
b) P(E) = 4 / 2^4 = 4 / 16 = 1/4 = 0.25
c) P(E) = 4/6 = 2/3 = 0.6667
d) P(E) = 0 /36 =0

6. a) P(Jupiter aligns with Mars) = 0.10
Answer: 0.10
b)P(J or M) = P(J) + P(M) - P(J and M)
0.80 = P(J) + 0.72 - 0.10
P(J) = 0.18
P(Jupiter not align with Mars) = P(Jupiter) - P(Jupiter and Mars) = 0.18 - 0.10 = 0.08
Answer: 0.08
c) P(Neither Jupiter aligns with Mars nor) = P(Jupiter or Mar)' = 1 - P(jupiter or Mars) = 1- 0.80 = 0.20
Answer: 0.20

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