Question

What is the probability of flipping at least one head? Round the answer to the nearhundredth of a percent.

Answer 1

At least 1 head means

1 H, 4 T

or

2 H, 3 T

or

3 H, 2 T

or

4 H, 1 T

or

5 H

We have to find each individual probabilty and add them. So, in probability notation:

P(1H,4T) + P(2H,3T) + P(3H,2T) + P(4H,1T) + P(5H)

Recall that probability of heads/tails in each flip is equal to 0.5

The flips are independent of each other. It doesn't matter what happened in 1 flip, it doesn't affect the next flip.

So,

P(1H,4T) = 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.03125

All other probabilties are same, thus:

`\begin{gathered} P\mleft(1H,4T\mright)+P\mleft(2H,3T\mright)+P\mleft(3H,2T\mright)+P\mleft(4H,1T\mright)+P\mleft(5H\mright) \\ =0.03125+0.03125+0.03125+0.03125+0.03125 \\ =0.15625 \end{gathered}`

In percentage:

0.15625 * 100 = 15.625%

Rounded to nearest hundredth,

15.63%