Question

A coin is flipped twice. True or false, the unconditional probability of getting tails on the secondflip is the same as the conditional probability of getting tails on the second flip given that the firstflip came up heads

Answer 1

Answer:  Given statement is TRUE.

Step-by-step explanation:

Let E and F represents  the events of getting tails on first flip and second flip respectively.

Then, we have

$P(E)=\dfrac{1}{2},\\\\\\P(F)=\dfrac{1}{2}.$

So, the unconditional probability of getting tails on the second flip is given by

$P(F)=\dfrac{1}{2}.$

And,  the conditional probability of getting tails on the second flip given that the first flip came up head is given by

$P(F/E')=\dfrac{P(F\cap E')}{P(E')}=\dfrac{\frac{1}{4}}{1-\frac{1}{2}}=\dfrac{\frac{1}{4}}{\frac{1}{2}}=\dfrac{1}{2}.$

Therefore, we get

$P(F)=P(F/E').$

Thus, the unconditional probability of getting tails on the second flip is the same as the conditional probability of getting tails on the second flip given that the first flip came up head.

Given statement is TRUE.