Two fair $4$-sided dice, one red and one green, are thrown. For each die, the faces are labelled \

Question

Two fair $4$-sided dice, one red and one green, are thrown. For each die, the faces are labelled $1, 2, 3, 4$. The score for each die is the number which lands face down. List the pairs of scores that give a sum of $6$. [3] Sum$2$$3$$4$$5$$6$$7$$8$ Probability$p$$q$$\frac{3}{16}$$\frac{4}{16}$$\frac{3}{16}$$r$$\frac{1}{16}$ Find the value of $p$, of $q$, and of $r$. Fred plays a game. He throws two fair $4$-sided dice four times. He wins a prize if the sum is $5$ on three or more throws. [3] Find the probability that Fred wins a prize.[6]

Accepted Answer

On each throw $P(\text{sum }5)=\frac4{16}=\frac14$. Therefore $P(Y\ge3)=\binom43(\frac14)^3(\frac34)+(\frac14)^4=0.05078$.

Build a dice-sum distribution and apply a binomial model to repeated throws.

Build a dice-sum distribution and apply a binomial model to repeated throws.

Solution:

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