Statistics And Probability Question 542
Question: A fair die is tossed repeatedly. A wins if it is 1 or 2 on two consecutive tosses and B wins if it is 3, 4, 5 or 6 on two consecutive tosses. The probability that A wins if the die is tossed indefinitely is
Options:
A) 1/3
B) 5/21
C) 1/4
D) 2/5
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Let P(S)=P(1 or 2) = 1/3 P(F) = P (3 or 4 or 5 or 6) = 2/3 P(A wins) = P[SS or S F SS or S F S F SS or …) Or (F S S or F S F S S or …)] $ =\frac{\frac{1}{9}}{1-\frac{2}{9}}+\frac{\frac{2}{27}}{1-\frac{2}{9}} $ $ =\frac{1}{9}\times \frac{9}{7}+\frac{2}{27}\times \frac{9}{7} $ $ =\frac{1}{7}+\frac{2}{21}=\frac{3+2}{21}=\frac{5}{21} $ P(A winning) $ =\frac{5}{21} $ , P(B winning) $ =\frac{16}{21} $
BETA
