The Anderson Lumber Company has three sawmills that produce boards of different lengths.The following table is a joint frequency distribution based on a random sample of 1000 boards selected from the lumber inventory. Based on these data,if three boards are selected at random,the probability that all three were made at sawmill A is:
A)0.037
B)0.334
C)1.00
D)0.556

Question

The Anderson Lumber Company has three sawmills that produce boards of different lengths.The following table is a joint frequency distribution based on a random sample of 1000 boards selected from the lumber inventory.  Based on these data,if three boards are selected at random,the probability that all three were made at sawmill A is:
A)0.037 
B)0.334 
C)1.00 
D)0.556

Quizplus · Accepted Answer

To find the probability that all three boards were made at sawmill A, we need to use the joint frequencies for Sawmill A where both the length and width are within the specified ranges for each of the three boards.

From the table, we see that there are 99 boards that meet these criteria for the first board, 88 boards for the second board (since one was already selected), and 77 boards for the third board (since two were already selected). Therefore, the probability of selecting three boards that were all made at sawmill A is:

(99/1000) * (88/999) * (77/998) ≈ 0.037.

Therefore, the best choice is A).

The Anderson Lumber Company Has Three Sawmills That Produce Boards