Explanation:
well, you have to make sure that the answer you enter is right.
so, pay attention and follow the lead here, so that you then can decide, if it is right or needs some adaptation.
every probability is always the ratio of desired cases to totally possible cases.
in our case here we have 10 balls in the back, one is pulled randomly.
so, there are 10 possible outcome cases.
(a)
the desired event X is to pull a white ball.
well, how many of the 10 possible balls are white ? this is the desired outcome.
3, 4, 5, 7, 8, 9, 10 : 7 balls are white.
so, in the line X you have to mark these 7 balls.
and the probability is : 7/10
"not X" : since we have only 2 types of balls, "not white" means "grey".
how many of the 10 possible balls are grey ?
1, 2, 6 : 3 balls are grey (not white).
so, in the line "not X" you have to mark these 3 balls.
and the probability is : 3/10
(b)
"1" always stands for the totally sure, always true event.
P(X) means the probability to get the event X as outcome.
again, in our case, X means pulling a white ball.
1 - P(X)
from (a) we know the probability to pull a white ball : 7/10.
so,
1 - P(X) = 1 - 7/10 = 10/10 - 7/10 = 3/10
and that stands for "probability for NOT pulling a white ball" in the sense of the "opposite of the probability to pull a white ball".
(c)
I don't know what options you can select, but it has to be something like
1 - P(X) is the same as P(not X).
simply because both mean the same :
the probabilty of the opposite of pulling a white ball is the probability of not pulling a white ball.