Question 4 A bag contains 4 red balls, 3 blue balls, and 3 green balls. John pla
ID: 3146863 • Letter: Q
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Question 4 A bag contains 4 red balls, 3 blue balls, and 3 green balls. John plays a series of games. In each game, he draws a ball from the bag. If the ball is red he wins Sb, otherwise he loses Sb. Assume that the balls drawn are replaced after each game, and John starts with $50 with the hope of reaching $100 at which point he will stop playing. If he loses all his money, the games also end. (a) Compute and demonstrate the probability that the series of games end with John being $50 richer than he had at the beginning if (4 marks) (ii) b=10; (3 marks) (ii) b=50. (3 marks)Explanation / Answer
a)
Probability for john winning one game= number of red balls/total balls = 4/10 = 2/5
b=1
Now, since john wins $1 if wins, he needs to play this game atleast 50 times to win $50 each will have a probability of 2/5.
therefore probability of John winning $50 = (2/5)50 = 1.26 * 10-20
ii) b=10
Similar to above, John would have to play atleast 5 games to win $50 each with probability 2/5.
therefore probability of John winning $50 = (2/5)5 =0.01024
iii) b=50
Similar to above, John would have to play atleast 1 game to win $50 each with probability 2/5.
Hence, with b=50, probability of john winning is 2/5 = 0.4
b) as we can see tht probability of john winning $50 is least in b=1 with 1.26 * 10-20 and maximum with b=50 at 0.4
With this our recommendation would be to play 1 game
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