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A physical therapist of Russian football team knows that the team will play 40% of its matches on artificial turf, this season. Because of his vast experience, he•knows that a football player's chances of incurring a knee injury is 50% higher if he is playing on artificial turf instead of grass. If the player's chances of a knee injury on artificial turf is 0.42, what is the probability that a football player with knee injury, incurred the injury while playing on grass?
Probability of playing on grass = 0.6
Probability of playing on Artificial turf = 0.4
Probability of injury on artificial turf = $$\frac{3}{2}$$(probability of injury on grass)
0.42 = $$\frac{3}{2}$$(probability of injury on grass)
Probability of injury on grass = 0.28
Applying Baye's theorem,
Probability of injury on grass = $$\ \frac{\ 0.6\times\ 0.28}{0.6\times\ 0.28+0.4\times\ 0.42}\approx\ 0.5$$
The answer is option C.
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