Suppose you toss 4 coins. What is the probability of getting 0 heads?

Answer 1

Hi Su,

The best way to approach a probability question like this is to first identify what they're asking for:

Let's let H = Heads, and T = Tails

This question asks what is the probability of getting no heads or:

Pr(0 H)

This is equivalent to getting tails on every throw, so:

Pr(0 H) = Pr(4 T) = Pr(4 not H)

We know each coin flip is an independent event, meaning the results of one coin toss do not affect any of the other trials. To answer this question, we then just need the probability of getting tails on any given throw. We know there's a 50/50 chance of getting either outcome so:

Pr(1 T) = 1/2

Because these are independent events:

Pr(4T) = Pr(1T)*Pr(1T)*Pr(1T)*Pr(1T) = (1/2)⁴ = 1/16

We defined Pr(4T) = Pr(0H) so,

The probability of getting zero heads in 4 coin flips is 1/16.