In a game a player rolls a biased four-faced die. The probability of each possible score is shown be

Question

In a game a player rolls a biased four-faced die. The probability of each possible score is shown below. Score 1 2 3 4 Probability $\frac15$ $\frac25$ $\frac1{10}$ $x$ Find the value of x. Find $E(X)$. The die is rolled twice. Find the probability of obtaining two scores of 3.

Accepted Answer

$E(X) = 1 \left(\frac{1}{5} \right)+2 \left(\frac{2}{5}\right)+3 \left(\frac{1}{10} \right)+4 \left(\frac{3}{10} \right)=2.5$. Two scores of 3 have probability $ \left(\frac1{10} \right)^2=0.01$.

Complete a biased-die distribution, calculate expectation and a repeated-roll probability.

Complete a biased-die distribution, calculate expectation and a repeated-roll probability.

Solution:

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