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What is the probability of getting exactly 3 heads if a fair coin is tossed 8 times?
The probability to get heads once is 1/2 as the coin is fair The probability to get heads twice is 1/2x1/2 The probability to get heads three times is 1/2x1/2x1/2 The probability to get tails once is 1/2 The probability to get tails 5 times is (1/2)5 So the probability to get 3 heads when the coin is tossed 8 times is (1/2)3(1/2)5=(1/2)8 = 1/256 If you read carefully you'll understand that 3 heads and 5 tails has the same probability than any other outcome = 1/256 As the coin is fair, each side has the same probability to appear So the probability to get 3 heads and 5 tails is the same as getting for instance 8 heads or 8 tails or 1 tails and 7 heads, and so on
What is the probability that a coin lands on its heads and tails?
The probability of the coin flip being heads or tails is 100%.
Was the outcome of getting heads or tails in the 20 tosses same as the probability ratio?
It depends on what variable the probability ratio was for! The random variable could have been the number of heads minus the number of tails, for example.
A fair nickel and a fair dice are tossed once outcomes match when both coins land on heads or both coins land on tails What is the theoretical probability of a match?
The probability of 2 coins both landing on heads or both landing on tails is 1/2 because there are 4 possible outcomes. Head, head. Head, tails. Tails, tails. Tails, heads. Tails, heads is different from heads, tails for reasons I am unsure of.
What is the expected number of flips of a coin to simulate a six-sided die?
Five coin flips. Any outcome on a six-sided die has a probability of 1 in 6. If I assume that the order of the outcome does not matter, the same probability can be achieved with five flips of the coin. The possible outcomes of five flips of a coin are as follows: 5 Heads 5 Tails 4 Heads and 1 Tails 4 Tails and 1 Heads 3 Heads and 2 Tails 3 Tails and 2 Heads For six possible outcomes.
