JEE PYQ: Probability Question 40
Question 40 - 2019 (12 Apr Shift 2)
A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:
(1) $\frac{1}{2}$ gain
(2) $\frac{1}{4}$ loss
(3) $\frac{1}{2}$ loss
(4) $2$ gain
Show Answer
Answer: (3)
Solution
$P(\text{doublet}) = \frac{6}{36} = \frac{1}{6}$. $P(\text{sum 9}) = \frac{4}{36} = \frac{1}{9}$. $P(\text{other}) = \frac{26}{36} = \frac{13}{18}$. $E = 15 \times \frac{1}{6} + 12 \times \frac{1}{9} + (-6) \times \frac{13}{18} = \frac{5}{2} + \frac{4}{3} - \frac{13}{3} = \frac{5}{2} - 3 = -\frac{1}{2}$. Loss of $\frac{1}{2}$.
BETA
