First slide

Theorems of probability

Question

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is:

Moderate

A

$\frac{1}{32}$
B

$\frac{3}{16}$
C

$\frac{1}{2}$
D

$\frac{5}{16}$

Solution

P(odd no. twice) = P(even no. thrice)
$\Rightarrow^{n} C_{2} {(\frac{1}{2})}^{n} =^{n} C_{3} {(\frac{1}{2})}^{n} \Rightarrow n = 5$
success is getting an odd number then P(odd successes) = P(1) + P(3) + P(5)
$=^{5} C_{1} {(\frac{1}{2})}^{5} +^{5} C_{3} {(\frac{1}{2})}^{5} +^{5} C_{5} {(\frac{1}{2})}^{5}$
$= \frac{16}{2^{5}} = \frac{1}{2}$

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