Question

What is the probability of obtaining 5 heads from 5 coin flips? Give your answer to 5 decimal places.

Answer 1

The probability of obtaining 5 heads from 5 coin flips is 0.03125.

Step-by-step explanation:

To calculate the probability of obtaining 5 heads from 5 coin flips, we need to determine the total number of possible outcomes and the number of favorable outcomes. In this case, we have 2 possible outcomes (heads or tails) for each coin flip, so the total number of possible outcomes for 5 coin flips is 2 x 2 x 2 x 2 x 2 = 32.

The number of ways to get 5 heads is 1, as there is only one combination of 5 heads.

Therefore, the probability of obtaining 5 heads from 5 coin flips is 1/32 = 0.03125 (rounded to 5 decimal places).

Answer 2

0.03125 = 3.125% probability of obtaining 5 heads from 5 coin flips.

Step-by-step explanation:

For each coin flip, there are only two possible outcomes. Either it is heads, or it is tails. The probabilities for each flip are independent from each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

In this problem we have that:

For each coin toss, heads and tails are equally as likely, so
`p = (1)/(2) = 0.5}`

What is the probability of obtaining 5 heads from 5 coin flips?

This is P(X = 5) when n = 5.

So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 5) = C_(5,5).(0.5)^(5).(0.5)^(0) = 0.03125`

0.03125 = 3.125% probability of obtaining 5 heads from 5 coin flips.