Step-by-step explanation:
come on, now, what do you think ?
the only tricky part is here the "or" condition.
again we have thankfully mutually exclusive attributes in the table, which allows us to simply add all numbers in the table for the total number of students.
so, we have
5+4×2×12 = 23 students as total possibilities.
how many of those 23 fulfill the criteria of paying a short or an instrument ?
everybody, who plays a sport is included, of course.
that is 5+2 = 7.
and then, everybody, who plays an instrument.
that is 5+4 = 9.
but careful, we have an overlap now. we cannot simply add both numbers, because there are 5 that play both, but we must not count them twice. they are still single students and pick choices after all.
so, for the desired cases we can only add the 4 from the 5+4 to the first 7 and get 7+4 = 11.
as a check : the complementary number should be the number of students that do not play either : 12.
so, yes, 11 + 12 = 23, and it all fits.
so, the probability to pick a student that plays a sport OR an instrument is
11/23 = 0.47826087...
