The blue marble should be worth 8 points , Option C is the answer.
Probability is the likeliness of an event to happen.
Let the random variable is x ,
probability mass function is f(x) = P(X = x)
then The expectation of a random variable is determined by
E(x) = ∑(i =1 to n) ( [tex]\rm x _i *f(x_i)[/tex] )
If the game has to be fair , the number of points that one can loose should be equal to the number of points one can gain.
Probability of getting any color marble = 1/5 = 0.2
Let x be the total points scored in a game
and b be the number of points for blue coloured marble
Probability of choosing non-blue marble = 4/5 (points =-2)
Probability of choosing blue marble = 1/5 (points = b)
E(x) = -2 * (4*5) + b* (1/5)
The expectation will be zero as the total points balance out
0 = -8/5 + b/5
b = 8
Therefore the blue marble should be worth 8 points , Option C is the answer.
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