Chapter 13.3, Problem 28AYU

Assigning Probabilities A coin is weighted so that tails is twice as likely as heads to occur. What probability should be assigned to heads? to tails?

To determine

What probability should be assigned to heads? To tails?

Answer to Problem 28AYU

$P\left(tails\right)=1/3$.

$P\left(heads\right)=2/3$.

Explanation of Solution

Given:

A coin is weighted so that tails is twice as likely as heads to occur.

Formula used:

${\displaystyle \sum }_{i=1}^{n}P\left(e_i\right)=P\left(e_1\right)+P\left(e_2\right)+\cdot \cdot \cdot +P\left(e_n\right)=1$

Calculation:

A coin is weighted so that tails is twice as likely as heads to occur.

Let $P\left(heads\right)=x$, $P\left(tails\right)=2x$.

Sum of the probability of individual event is 1.

$P\left(tails\right)+P\left(heads\right)=3x=1$

$x=\frac{1}{3}$

$P\left(tails\right)=1/3$.

$P\left(heads\right)=2/3$.