Question

Question: What probability should be assigned to the outcome of heads when a biased coin is tossed, if heads is three times as likely to come up as tails? What probability should be assigned to the outcome of tails?

Short answer

Answer

The probability that should be assigned to the outcome of heads when a biased coin is tossed, if heads is three times as likely to come up as tails, is $\frac{3}{4}$and the probability that should be assigned to the outcome of tails is, $\frac{1}{4}$.

Step-by-step solution

 Given  

Given that the heads are three times as likely to come up as tails.

The Concept of Probability

If$\mathit{S}$represents the sample space and$\mathit{E}$ represents the event. Then the probability of occurrence of favourable event is given by the formula as below:

$\mathit{P}\mathbf{\left(}\mathit{E}\mathbf{\right)}\mathbf{=}\frac{\mathbf{n}\mathbf{\left(}\mathbf{E}\mathbf{\right)}}{\mathbf{n}\mathbf{\left(}\mathbf{S}\mathbf{\right)}}$

Determine the probability

As per the problem we have been asked to find that the probability that should be assigned to the outcome of heads when a biased coin is tossed, if heads is three times as likely to come up as tails and the probability that should be assigned to the outcome of tails.

If $S$represents the sample space and $E$represents the event. Then the probability of occurrence of favourable event is given by the formula as below:

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Given that, heads are three times as likely to come up as tails,$3+1=4=n\left(S\right)$.

Event of getting heads is three times as likely to come up as tails,

$n\left(E\right)=3.$

Now substitute the values in the above formula we get, Probability of getting a head is$P\left(E_H\right)=\frac{3}{4}\text{.}$

Event of getting a tail,$n\left(E\right)=1$

Now substitute the values in the above formula we get, Probability of getting tail is,

$P\left(E_T\right)=\frac{1}{4}$

The probability that should be assigned to the outcome of heads when a biased coin is tossed, if heads is three times as likely to come up as tails, is$\frac{3}{4}$ and the probability that should be assigned to the outcome of tails is,$\frac{1}{4}$ .