JEE PYQ: Probability Question 7
Question 7 - 2021 (24 Feb Shift 1)
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:
(1) $\frac{3}{16}$
(2) $\frac{1}{2}$
(3) $\frac{5}{16}$
(4) $\frac{1}{32}$
Show Answer
Answer: (2)
Solution
$P = \frac{1}{2}$. ${}^nC_2 \left(\frac{1}{2}\right)^n = {}^nC_3 \left(\frac{1}{2}\right)^n \Rightarrow {}^nC_2 = {}^nC_3 \Rightarrow n = 5$. $P(\text{odd times}) = {}^5C_1\left(\frac{1}{2}\right)^5 + {}^5C_3\left(\frac{1}{2}\right)^5 + {}^5C_5\left(\frac{1}{2}\right)^5 = \frac{16}{32} = \frac{1}{2}$.
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