An athlete has 75% of winning the race if he is not injured. if he is injured, his probability of winning the race is only 15%. if he total chances of winning is 51%, what is the probability that he gets injured?
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Let....
X = 'is the athlete injured' (X in {0,1})
⇒ (0 means not injured, 1 means injured)
Y = 'the athlete wins' (Y in {0,1})
⇒ (0 means not wins , 1 means wins the race)
Given,
i) P(Y=1|X=0) = 0.75
ii) P(Y=1|X=1) = 0.15
iii) P(Y=1) = 0.51
so,
P(X=1) = 1-P(Y=1) ⇒ 1-0.51
⇒0.49
We are looking for P(X=1) - P(Y=1) = P(Y=1|X=0)*(1-P(X=1)) + P(Y=1|X=1)*P(X=1)
⇒ P(X=1) - P(Y=1) = (0.75*0.49) + (0.15*0.49) ⇒ 0.4
The above equation should provide you with the answer 0.4!
>>Hope this helps!!... :)
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