a coin is tossed 3 times. find the probability that all 3 tosses are tails?

Answer 1

P(3 tails) = (1/2) (1/2) (1/2) = 1 / 8

Answer 2

Let X be the number of tails

X has the binomial distribution with n = 3 trials and success probability p = 0.5 (assuming a fair coin).

In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.

this is found by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.
Or, to be more accurate, the binomial is the sum of n independent and identically distributed Bernoulli trials.

the mean of the binomial distribution is n * p
the variance of the binomial distribution is n * p * (1 - p)

In this question you have:

P(X = 0 ) = 0.125 = P(no tosses are tails)
P(X = 1 ) = 0.375 = P(one tosses is a tail)
P(X = 2 ) = 0.375 = P(two tosses are tails)
P(X = 3 ) = 0.125 = P(all three tosses are tails)

Answer 3

it would be 1/2^3 or 1/8

Answer 4

1/27

Answer 5

=(1/2)*(1/2)*(1/2)
=1/8

Answer 6

.125 (1/8)