Abox contains 6 nuts, 8 bolts, and 4 screws. if 3 objects are selected in succession randomly, what is the probability of selecting a nut, then a bolt, then a screw, if replacement occurs each time? a. 8/243 b. 16/243 c. 1/27 d. 1

The answer is A. 8/243

There are in total 18 objects:
6 nuts + 8 bolts + 4 screws = 18 objects

The probability of choosing a nut is: 6/18 (since there are 6 nuts of total 18 objects).
The probability of choosing a bolt is: 8/18 (since there are 6 bolts of total 18 objects).
The probability of choosing a screw is: 4/18 (since there are 4 screws of total 18 objects).

Because replacement occurs each time, there are always 18 objects. Also, since selecting a nut, a bolt, and a screw occurs together, we will use the multiplication rule and multiply the probabilities of events occurring together:

For the first question the answer is a, for the second c, for the third d, for the 4th b, for the 5th a