# Biased coin

• Mar 18th 2011, 04:51 PM
Natasha1
Biased coin
Ben spins a biased coin twice. The probability that it will come down heads both times is 0.36

What is the probability that it will come down tails both time?

Is it 1 - 0.36 = 0.64
• Mar 18th 2011, 05:49 PM
alexmahone
Quote:

Originally Posted by Natasha1
What is the probability that it will come down tails both time?

Is it 1 - 0.36 = 0.64

No.

$(p_H)^2=0.36$

$p_H=0.6$

$p_T=1-p_H=1-0.6=0.4$

Probability that it will come down tails both time is $(p_T)^2=0.16$
• Mar 18th 2011, 06:39 PM
Quacky
Quote:

Originally Posted by Natasha1
Ben spins a biased coin twice. The probability that it will come down heads both times is 0.36

What is the probability that it will come down tails both time?

Is it 1 - 0.36 = 0.64

It isn't a very significant addition to what Alex said, but the reason your method is incorrect is that you haven't considered the two possible scenarios whereby you could obtain exactly one head and one tail.
• Mar 18th 2011, 10:56 PM
CaptainBlack
Quote:

Originally Posted by Natasha1
Ben spins a biased coin twice. The probability that it will come down heads both times is 0.36

What is the probability that it will come down tails both time?

Is it 1 - 0.36 = 0.64

Let $p$ be the probability that the coin comes down heads on a single flip. Then the probability that it comes down heads on two consecutive flips is:

$p^2=0.36$

The probability that it comes down tails on two consecutive flips is: $(1-p)^2$.....

and the rest is algebra

CB