A game is played, where a die is tossed and a marble selected from a bag. Bag $M$ contains $3$ r

Question

A game is played, where a die is tossed and a marble selected from a bag. Bag $M$ contains $3$ red marbles $(R)$ and $2$ green marbles $(G)$. Bag $N$ contains $2$ red marbles and $8$ green marbles. A fair six-sided die is tossed. If a $3$ or $5$ appears on the die, bag $M$ is selected $(M)$. If any other number appears, bag $N$ is selected $(N)$. A single marble is then drawn at random from the selected bag.

Copy and complete the probability tree diagram on your answer sheet.[3]
[7]
1. Write down the probability that bag $M$ is selected and a green marble drawn from it.
2. Find the probability that a green marble is drawn from either bag.
3. Given that the marble is green, calculate the probability that it came from Bag $M$.
A player wins $\$2$ for a red marble and $\$5$ for a green marble. What are his expected winnings?
[4]

Accepted Answer

Since $P(R)=\frac13$, expected winnings are $2(\frac13)+5(\frac23)=4$ dollars.

Complete a two-stage tree, calculate total/Bayes probabilities and expected winnings.

Complete a two-stage tree, calculate total/Bayes probabilities and expected winnings.

Solution:

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