Prove by induction that 7^2n+1 +1 is divisible by 8, for all nEN
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Answer:
The expected value of rolling a 5 or 6 is 10.
Step-by-step explanation:
The sample space of rolling a standard number cube is:
S = {1, 2, 3, 4, 5 and 6}
The cube is standard, this implies that each side has an equal probability of landing face-up.
So, the probability of all the six outcomes is same, i.e. .
Now it is provided that Apu rolls the cube <em>n</em> = 30 times.
Let the random variable <em>X</em> represent the value on the face of cube.
The event of rolling a 5 and rolling a 6 are mutually exclusive, i.e. they cannot occur together.
So, P (X = 5 and X = 6) = 0.
Compute the probability of getting a 5 or 6 as follows:
P (X = 5 or X = 6) = P (X = 5) + P (X = 6) - P (X = 5 and X = 6)
= P (X = 5) + P (X = 6)
Compute the expected value of rolling a 5 or 6 as follows:
Thus, the expected value of rolling a 5 or 6 is 10.