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In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.
For the situation given in the equation, we have:
Probability of getting a six in a throw of a die
Also, probability of not getting a 6
Now, there are three cases from which the expected value of the amount which he wins can be calculated:
(i) First case is that, if he gets a six on his first through then the required probability will be
∴ Amount received by him = Rs. 1
(ii) Secondly, if he gets six on his second throw then the probability
∴ Amount received by him = - Rs. 1 + Rs. 1
= 0
(iii) Lastly, if he does not get six in first two throws and gets six in his third throw then the probability
∴ Amount received by him = - Rs. 1 – Rs. 1 + Rs. 1
= - 1
Hence, expected value that he can win
Suppose we have four boxes A, B, C and D containing coloured marbles as given below:
Box | Marble colour | ||
Red | White | Black | |
A | 1 | 6 | 3 |
B | 6 | 2 | 2 |
C | 8 | 1 | 1 |
D | 0 | 6 | 4 |
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?