The American Journal of Sports Medicine published a study of 810 women collegiate rugby players with two common knee injuries: medial cruciate ligament (MCL) sprains and anterior cruciate ligament (ACL) tears. For backfield players, it was found that 39% had MCL sprains and 61% had ACL tears. For forwards, it was found that 33% had MCL sprains and 67% had ACL tears. Since a rugby team consists of eight forwards and seven backs, you can assume that 47% of the players with knee injuries are backs and 53% are forwards.
a. Find the unconditional probability that a rugby player selected at random from this group of players has experienced an MCL sprain.
b. Given that you have selected a player who has an MCL sprain, what is the probability that the player is a forward?
c. Given that you have selected a player who has an ACL tear, what is the probability that the player is a back?