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Question 1
What is the probability that if you roll two six-sided die and toss three coins at the same time, we
will get at least one head on a coin and no pairs on the dice?
Solution.
π·π(ππ πππππ πππ ππππ
πππ
ππ πππππ ππ π
ππ) is:
= π·π(ππ πππππ πππ ππππ
ππ π πππππ) Γ π·π(ππ ππππ ππ π
ππ)
For the three coins (πΆ1 , πΆ2 πππ πΆ3 ), all the possible outcomes are:
C1 C2 C3 β HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
β΄ Pr(at least 3 heads) =
number of outcome with one or more heads
7
=
total number of outcomes
8
For the two six-sided die, there are a possible of 36 different outcomes. Since we do not want a
pair on the die, six of the outcomes, (1, 1), (2, 2), (3, 3), (4, 4), (5, ...