Question

What is the probability you will get one tail? Toss a coin three times

Answer 1

3/8

Explanation:

We want the probability of getting a tail in three trials.

We will use binomial distribution, given by the formula:

`\displaystyle P(x)={n\choose x}p^xq^(n-x)`

We want one success out of three trials. So, n = 3 and x = 1.

The probability for success in one trial is 1/2. So, p = 1/2.

And the probability for failure in one trial is 1/2. q = 1/2.

Therefore, the probability of getting a tail is:

`\displaystyle P(1)={3\choose 1}\Big((1)/(2)\Big)\Big((1)/(2)\Big)^2`

Evaluate:

`\displaystyle P(1)=3\Big((1)/(8)\Big)=(3)/(8)`

The probability of getting a tail by tossing a coin thrice is 3/8.

Edit:

My apologies. If you haven't learned the binomial distribution yet, below is another method.

Using the fundamental counting principle, we have a total of 2 times 2 times 2 or 8 total outcomes.

We want only one tail. This can be the first toss, the second toss, or the third toss.

So, out of 8 total outcomes, only 3 are favorable.

Hence, the probability of getting one tail by tossing a coin thrice is 3/8.