0
More than 140 rolls will be required if and only if the sum of the first 140 rolls does not exceed 400
Let S = X1 + X2 + ... + X140 where Xi is the number obtained in the ith rollNote E[X] = 7/2, Var[X] = 35/12
So E[S] = 140(7/2) = 490, Var[S] = 140(35/12) = 1225/3
By Central Limit Theorem, (with continuity correction)
Pr{S ≤ 400}
≈ Pr{Z < (400.5 - 490)/√(1225/3)}
≈ 4.731327 * 10^(-6)
Still curious? Ask our experts.
Chat with our AI personalities
Blake
Vivi
DevinAdd your answer:
Earn +20 pts
What are equally likely events in probability?
If there are two possible outcomes, the probability would be 50% or 1/2 (AN EVEN CHANCE). "Equally likely events" refers to the chances of each possible outcome among many being equal. For example, using a six-sided die in a dice game yields a 1/6 chance for any one of the numbers to appear on top of the cube. Assuming that the die is not loaded, all six numbers are presumed to have an equal likelihood to end up on top in a given throw.
If you roll a die what is the probability that a three will appear on top?
I think it's 1 out of 6 chance.
If a die is rolled 60 times what is the probability of having a 2 appear at least 9 times?
It is 1 - 0.3120 = 0.6880, approx.
A fair coin is tossed 9 times What is the probability that At least two heads appear?
well, it will have 6 times of the greater chance.
You toss three coins What is the probability of the event 3 Heads appear?
Since each event is independent (heads in one coin does not affect the probability of the other two coin flips), the multiplication rule applies: 1/2 x 1/2 x 1/2 = 1/8 or 0.125. So we can say the probability is 12.5%.
