Two dies are thrown simultaneously if x denote the numbers of sixes. Find the expectation of x
kavya jain
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Probability of a six for on one die : 1/6
probability of a non-six on one die : 5/6
The number of possibilities for two dies:
0 number of sixes on both together: 5/6 * 5/6 = 25/36
1 number of sixes from both together: 1/6* 5/6 + 1/6 * 5/6 = 10/36
2 number of sixes from both together: 1/6 * 1/6 = 1/36
Sum of the above 3 probabilities is 1.
X = event that X sixes occur when two dies are thrown.
Expected value of X = Summation of X * Probability of X
= 0 * 25/36 + 1 * 10/36 + 2 * 1/36 = 12/36 = 1/3
probability of a non-six on one die : 5/6
The number of possibilities for two dies:
0 number of sixes on both together: 5/6 * 5/6 = 25/36
1 number of sixes from both together: 1/6* 5/6 + 1/6 * 5/6 = 10/36
2 number of sixes from both together: 1/6 * 1/6 = 1/36
Sum of the above 3 probabilities is 1.
X = event that X sixes occur when two dies are thrown.
Expected value of X = Summation of X * Probability of X
= 0 * 25/36 + 1 * 10/36 + 2 * 1/36 = 12/36 = 1/3
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