A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i)
with replacement (ii) without replacement. The probability that the first draw would
produce white balls and the second draw would produce black balls are respectively
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(i) Regarding the occurrence as a simple event, the chance =(5×7)÷
12
C
2
=
66
35
.
(ii) The occurrence may be regarded as the happening of one or other of the two following compound events:
(1) drawing a white and then a black ball, the chance of which is
12
5
×
11
7
or
132
35
;
(2) drawing a black and then a white ball, the chance of which is
12
7
×
11
5
, or
132
35
.
And since these events are mutually exclusive, the required chance =
132
35
+
132
35
=
66
35
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