Question

A box 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

Answer 1

Answer:

Step-by-step explanation:

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).

Answer 2

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:
$P= \frac{6}{18} *\frac{8}{18} *\frac{4}{18} =\frac{1}{3} *\frac{4}{9} *\frac{2}{9} =\frac{8}{243}$