In a soccer match, the probability of a player completing a full warm-up is 0.8 and that of not completing a full warm-up is 0.2. The probability of not sustaining any cramps when a full warm-up is done is 0.7 while the probability of sustaining a cramp, when the warm-up is incomplete, is 0.9. Using a probability tree or otherwise,

a. Find the probability that a player suffers from a cramp in the soccer match.

b. Given that a player has a cramp, find the probability that he did not complete his warm-up.

c. Given that a player did not suffer a cramp, find the probability that he c

Question

In a soccer match, the probability of a player completing a full warm-up is 0.8 and that of not completing a full warm-up is 0.2. The probability of not sustaining any cramps when a full warm-up is done is 0.7 while the probability of sustaining a cramp, when the warm-up is incomplete, is 0.9. Using a probability tree or otherwise,

a.    Find the probability that a player suffers from a cramp in the soccer match.
 
b.    Given that a player has a cramp, find the probability that he did not complete his warm-up.
 
c.    Given that a player did not suffer a cramp, find the probability that he c