The probability is 5/16.
The empirical probability can only be determined by carrying out the experiment a very large number of times. Otherwise it would be the theoretical probability.
It is 3/4 or 0.75
Each toss has a 1/2 probability of getting heads. Each toss is an independent event. So three heads in a row (heads AND heads AND heads) would have a probability of:1/2 * 1/2 * 1/2 = (1/2)^3 = 1/(2^3) = 1/8 = 12.5%
The probability of tossing 6 heads in 6 dice is 1 in 26, or 1 in 64, or 0.015625. THe probability of doing that at least once in six trials, then, is 6 in 26, or 6 in 64, or 3 in 32, or 0.09375.
3 out of 6
The probability is 5/16.
P(Heads) = 2/3
There are 23 or 8 possibilities; one is HHH. So, probability of HHH is 1/8 or 0.125.
It is (1/2)3 = 1/8 or 0.125
The empirical probability can only be determined by carrying out the experiment a very large number of times. Otherwise it would be the theoretical probability.
It is 3/8.
It is 3/4 or 0.75
Each coin toss is a Bernoulli trial with a probability of success of .5. The probability of tossing heads exactly 3 times out of five is3 ~ Bin(5, 1/2), which equals(5!/(3!(5-3)!))(0.5^3)(1-0.5)^(5-3), which is 0.3125.
Each toss has a 1/2 probability of getting heads. Each toss is an independent event. So three heads in a row (heads AND heads AND heads) would have a probability of:1/2 * 1/2 * 1/2 = (1/2)^3 = 1/(2^3) = 1/8 = 12.5%
The probability of tossing 6 heads in 6 dice is 1 in 26, or 1 in 64, or 0.015625. THe probability of doing that at least once in six trials, then, is 6 in 26, or 6 in 64, or 3 in 32, or 0.09375.
First event is to roll a 3 or 6 on a die, which gives you a probability of 2 out of 6. Second event is tossing a heads on a coin, so a probability of 1 out of 2. Since both chances are not related, you can multiply both chances: 2/6 times 1/2 = 1/6 = 0,166666...