Probability topic

Question

odds against to an event R will occur is 3:2 which of the following could be the Probability of events R and E will occur is

 

(a)0.32

(b)0.88

(c)0.44

(d)0.56
(e)0.40

Answer 1

The odds against R occurring are 3:2.  That means the Probability of R not occurring is 3/(3+2) or 3/5 or 60% or 0.60.

So, the probability of event R happening is one minus that value (because 1 is certainty).  So, the Probability of R occurring is 0.4.

 

The problem asks us about the Probability of both events R and E occurring.  If the Probability of event E occurring is larger than zero, then that reduces the Probability of both events R and E occurring simultaneously (because event E could possibly occur when event R did not).  So, the answer must be less than or equal to 0.40.

 

That leaves only (a) 0.32 and (e) 0.40 as choices.  If it is a safe assumption that event E has some non-aero probability of occurring, then the single answer is (a) 0.32.  But if event E will never occur (so why is it even mentioned?), then both (a) 0.32 and (e) 0.40 would be answers.  The given odds against event R are too great for answers (b), (c), and (d) to be possible.