For this problem were given the total number of putts as one million, 613,234 were given that the number of pets made or 983,764 and the number of putts missed or 629,470. We're also told that the probability of the shot being part given that the cut was made his 0.64 the probability of the putt being a birdie, given that it was, made his 0.188 The probability of the putt being part, given that it was missed, his 0.203 and the probability of the pup being a birdie. Given that it was made this 0.734 hurt a asks what's the probability that the player makes a putt to calculate that we take the number of favorable outcomes divided by the total number of outcomes. So the number of favorable outcomes are the number of players that made the putt. So 983,764 divided by the total number of putts, which is one million, 613,234 to give a probability of making the putt as 0.6098 Part B says suppose that a player has a putt for par. What's the probability of the player will make the putt do this? We're going to use Berry space there, so to calculate the probability of making the putt. Given that it's par, we say that that's equal to the probability of a being part, given that the putt was made times the probability of being made divided by the probability of a being part, given that it was made times the probability of being made, plus the probability of it being part given that it was missed times the probability of it being missed. To calculate this, we need to know the probability of the shot being missed. So we take the number of favorable outcomes divided by the total number of outcomes. So the number of what's that were missed was there. 629,470 divided by the total number of putts, which is 1,613,234 to give a probability of a pup being missed as 0.3902 We can then take the probabilities above, plus the calculated probabilities of a pup being made or missed and plug it in to the equation. So the probability of making the shot given the shot was par. We 0.64 times. 0.6098 divided by 0.64 times. 0.6098 plus 0.203 times 0.3902 To give a probability of 18313 Part C says suppose that a player has a putt for birdie. What is the probability that the player will make the putt we again use based here? Um so the probability of making the putt, given that it's birdy is equal to the probability the pup being birdie. Given that it's made times the probability of the pup being made divided by the probability of the pup being birdie, given that it was made times, the probability of it being made, plus the probability of the putt being birdie. Given that it was missed times the probability of being missed putting in the numbers given by the problem and calculated above, we get the probability to be 0.188 times, 0.609 e divided by 0.188 times 0.6 year 98 plus 980.734 times 0.3902 To give a probability, a 0.285 nights party asks us to comment on the differences in probabilities from Parts B and C. So in part B, the probability of making a putt given that the shot is par is 0.8313 Well, for part C. The probability of making a putt given that it's Birdy is 0.2859 Therefore, you have a higher probability of making a shot when taking a par putt, then when making a birdie putt.