JEE PYQ: Probability Question 5
Question 5 - 2021 (17 Mar Shift 2)
Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $\frac{1}{2}$ and probability of occurrence of 0 at the odd place be $\frac{1}{3}$. Then the probability that ‘10’ is followed by ‘01’ is equal to:
(1) $\frac{1}{18}$
(2) $\frac{1}{3}$
(3) $\frac{1}{6}$
(4) $\frac{1}{9}$
Show Answer
Answer: (4)
Solution
Pattern “1001”: positions alternate odd/even. $P = \left(\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2} \cdot \frac{2}{3}\right) + \left(\frac{2}{3} \cdot \frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2}\right) = \frac{1}{9}$.
BETA
