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When two coins are tossed simultaneously what is the probability of obtaining at most one head?
The probability is 3/4.
What is the probability of obtaining exactly two heads in three flips of a coin given that at least one is a head?
The probability of obtaining exactly two heads in three flips of a coin is 0.5x0.5x0.5 (for the probabilities) x3 (for the number of ways it could happen). This is 0.375. However, we are told that at least one is a head, so the probability that we got 3 tails was impossible. This probability is 0.53 or 0.125. To deduct this we need to divide the probability we have by 1-0.125 0.375/(1-0.125) = approximately 0.4286
Probability of getting one head and two tails on a toss of three fair coins?
50%
What is the probability of getting a run of three consecutive heads before a run of two consecutive tails when tossing a fair coin over and over?
The probability of getting a head first time is one out of two, or a half. The probability of getting a head the next time is still one out of two, so the combined probability is one quarter. Similarly, one eighth is the probability of getting three in a row; but the pattern does not end there, the probability of getting a tails the next time is STILL one in two, so that is a one in sixteen chance of that run, the probability of the entire sequence is therefore one in thirty-two.
What is the probability of tossing a coin 5 times and getting at least one tail and one head?
This is one of those cases where it is probably easier to think what is the probability of not doing it, then subtracting that from 1 to get the probability of doing it. To not get at least one head and one tail, you would have to get all heads or all tails. To get all heads, the probability is (1/2)5. To get all tails is the same probability; so double it to get the probability of either of those. 2(1/2)5=1/16. Subtract the 1/16 from 1 to get 15/16. Answer: 15/16
