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Two fair dice are each numbered so that they have the numbers 1 3 5 7 9 and 11 how many ways are there of scoring a total of 16?
5 + 11 11 + 5 7 + 9 9 + 7 So 4 ways if you are allowed to throw each die only once. But the question did not state that assumption; so the additional ways are: Throw die #1 16 times and get 1 each time. Throw die #2 16 times and get 1 each time. Throw die # 1 13 times and get 1 13 times and 3 once. Throw die # 2 13 times and get 1 13 times and 3 once. Throw die #1 13 times and get 1 each time, then throw die # 2 once and get 3. Throw die #1 12 times and get 1 each time, then throw die #2 once and get 3, then throw die #1 again and get another 1. You get the idea, figure out the rest yourself.
What is your mathematical expectation if you win 6 when a die come up 1 or 2 3 4 5 or 6?
If it is an ordinary die, it must come up 1 or 2, 3, 4, 5 or 6 so you must win 6 whatever happens. The expectation, therefore, is 6 for each throw of the die.
What is the probability that 3 heads come up on a throw of 3 dice?
The probability is very, very small, because there are no heads marked anywhere on the dice.
Bamboo can grow up how much in 24 hours?
3 cm
What is the probability that 12 rolls of a die will show exactly three fours?
When a die is rolled once, the probability of a 4 showing up is 1/6. Apply the binomial probability for finding the probability of exactly three fours out of 12 throws of a die. n=12 (number of throws) p=1/6 (probability of a four in a single throw) x = 3 (number of times out of 12 , a four showing up) P(x=3) = 12C3 (1/6)^3 (5/6)^(12-3) = 12C3 (1/6)^3 (5/6)^9 = 0.197443
