Answer:
P(2U5) = 7/21 = 1/3
the probability of getting either a 5 or a 2 in one throw is 1/3
Step-by-step explanation:
Given that; the probability of each face turning up is proportional to the number of dots on that face
P(1) = 1×P(1)
P(2) = 2×P(1)
P(3) = 3×P(1)
P(4) = 4×P(1)
P(5) = 5×P(1)
P(6) = 6×P(1)
P(T) = 21×P(1)
Where;
P(x) is the probability of getting number x on the dice.
P(T) is the total probability of obtaining any number
N(x) is the number of possible number x in terms of the distribution function.
P(x) = N(x)/N(T) ....1
And since P(T) is constant, and P(T) is proportional to N(T) then,
P(x) is directly proportional to N(x)
So, equation 1 becomes;
P(x) = N(x)/N(T) = P(x)/P(T) ....2
The probability of getting either a 5 or a 2 in one throw
P(2U5) = (P(2) + P(5))/P(T)
Substituting the values of each probability;
P(2U5) = (2P(1) + 5P(1))/21P(1)
P(2U5) = 7P(1)/21P(1)
P(1) cancel out, to give;
P(2U5) = 7/21 = 1/3
the probability of getting either a 5 or a 2 in one throw is 1/3
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