Final answer:
The probability of the basketball player missing the shot is 9/31 since it's calculated by dividing the number of ways he can miss (9 ways) by the total number of outcomes (31 ways).
Step-by-step explanation:
The odds of the basketball player making the shot are given as 22:9. To find the probability of the player missing the shot, we first need to find the total number of possible outcomes, which is the sum of the two numbers in the odds, that is, 22 (for making the shot) plus 9 (for missing the shot), giving us a total of 31 possible outcomes.
Since the probability is the ratio of the number of favorable outcomes to the total number of possible outcomes, the probability of the player missing the shot is the number of ways he can miss (9 ways) out of the total number of possible outcomes (31 ways).
Therefore, the probability of him missing the shot is 9/31, which corresponds to option A.