Question

if a fair coin ts tossed 6 times, find the probability that number of heads is none
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Answer 1

Answer:

Let X represent the number of times a coin comes up heads. Assuming that the probability that heads and tails are equal, then X follows a binomial distribution with n = 6 and p = 0.5.

The probability mass function for a binomial distribution is

P(X = x) = (nx)pxqn−x

where n is the number of trials, x is the number of successes (for this problem we consider getting a head as a success), p is the probability of success and q is the probability of failure (where q = 1 - p).

To find the probability of getting at least one head, you can do the following:

(The first equality below is due to the complement rule P(A) = 1 - P(A’) where A’ is the complement of the event A.)

P(X ≥ 1) = 1 - P(X < 1)

=1− P(X=0)

60)(0.5)0(0.5)6

=0.984375

You can also do this in R, by doing the following:

1 - dbinom(x=0,size = 6,prob = 0.5)

and you get the same answer of 0.984375.

The probability of getting all heads is

P(X = 6) = (66)(0.5)6(0.5)0

=0.015625

Step-by-step explanation:

The line of code below shows how you can do this in R

dbinom(x=6,size = 6,prob = 0.5)

Again, you get the answer for P(X = 6) to be 0.015625.