First slide

Random variable and probability distribution

Question

A die is thrown a fixed number of times. If probability of getting even number 3 times is same as the probability of getting even number 4 times, then probability of getting even number exactly once is

Moderate

A

1/6
B

1/9
C

5/36
D

7/128

Solution

According to the given condition,
$^{n} C_{3} {(\frac{1}{2})}^{n} =^{n} C_{4} {(\frac{1}{2})}^{n}$ ,
where n is the number of times die is thrown.
$∴^{n} C_{3} =^{n} C_{4} \Rightarrow n = 7$
Thus, the required probability is
$=^{7} C_{1} {(\frac{1}{2})}^{7} = \frac{7}{2^{7}} = \frac{7}{128}$

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