First slide

Theorems of probability

Question

A six-faced fair dice is shown until 1 comes. Then the probability that 1 comes in even number of trials is

Moderate

A

5/11
B

5/6
C

6/11
D

1/6

Solution

In single throw of a dice, probability of getting 1 is 1/6 and probability of not getting 1 is 5/6.
Then, getting 1 in even number of chances is getting 1 in 2nd
chance or in 4th chance or in 6th chance and so on.
Therefore, the required probability is
$\begin{array}{l} \frac{5}{6} \times \frac{1}{6} + {(\frac{5}{6})}^{3} \times \frac{1}{6} + {(\frac{5}{6})}^{5} \times \frac{1}{6} + \dots + \infty \\ = \frac{5}{36} [\frac{1}{1 - \frac{25}{36}}] \\ = \frac{5}{36} \times \frac{36}{11} \\ = \frac{5}{11} \end{array}$

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