Question

What is the probability of getting zero heads in six tosses? What is the probability of getting exactly two heads in six tosses? (Hint: these are probability questions, not questions about your particular simulation. You can either compute the probabilities by hand, or you can compute binomial probabilities P(X = k) using Minitab by typing the value or values of k into some column, going to Calc --> Probability Distributions --> Binomial, typing the values for n and p into the appropriate boxes, and listing as the "Input Column" the column in which you typed the values of k. Also make sure to select the bubble "Probability". If the bubble "Cumulative probability" is selected instead, then Minitab will give you P(X ≤ k).)

Answer 1

The probability of getting zero heads in six tosses is 0.015625.

The probability of getting exactly two heads in six tosses is 0.234375.

Explanation:

Using the Minitab software for computing the desired probabilities.

We take n=6 and p=1/2 because we have six tosses and in binomial distribution the probability of success p remains constant in each trial whereas the probability of success in this case is getting heads.

When a coin is tossed then there are two possible outcomes head or tail.

So,

p= P(heads)=1/2=0.5

The probability of getting zero heads in six tosses is computed by considering the following steps:

In Minitab

Calc >Probability Distributions > Binomial

Select n=6 and p=0.5 and select input constant=0 and bubble the probability and by clicking OK we get the following output:

Probability Density Function

Binomial with n = 6 and p = 0.5

x P( X = x )

0 0.015625

So, the probability of getting zero heads in six tosses is 0.015625.

The probability of getting exactly two heads in six tosses is computed by considering the following steps :

In Minitab

Calc >Probability Distributions > Binomial

Select n=6 and p=0.5 and select input constant=2 and bubble the probability and by clicking OK we get the following output:

Probability Density Function

Binomial with n = 6 and p = 0.5

x P( X = x )

2 0.234375

So, the probability of getting exactly two heads in six tosses is 0.234375.