Probability Question 221
Question: The odds against a certain event is 5 : 2 and the odds in favour of another event is 6 : 5. If both the events are independent, then the probability that at least one of the events will happen is
[RPET 1997]
Options:
A) $ \frac{50}{77} $
B) $ \frac{52}{77} $
C) $ \frac{25}{88} $
D) $ \frac{63}{88} $
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ A $ and $ B $ be two given events.
The odds against $ A $ are $ 5:2 $ , therefore $ P(A)=\frac{2}{7} $ .
The odds in favour of $ B $ are $ 6:5 $ , therefore $ P(B)=\frac{6}{11}. $
The required probability $ =1-P(\bar{A})P(\bar{B}) $
$ =1-( 1-\frac{2}{7} )( 1-\frac{6}{11} )=\frac{52}{77}. $
BETA
