Question

A fair coin is tossed repeatedly. if tail appears 3 times, what is the probability that head will appear in the 4th

Answer 1

According to the given question the favourable outcome is [TTTH]
Probability of getting the first, second and third tail is $\frac{1}{2}$ each and probability of getting fourth head is also $\frac{1}{2}$.
So the probability of getting each of these one after the other is = $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}$=$\frac{1}{16}$

Alternate method-

Total number of outcomes on throwing a coin 4 times = 2⁴

Now number of favourable outcomes that is 3 tail and then head = 1​

$$\begin{gathered} P\left(\mathrm{getting}4\mathrm{th}\mathrm{head}\mathrm{after}3\mathrm{tails}\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}} \\ =\frac{1}{16} \end{gathered}$$