Reference no: EM132230940

Brinell & Rockwell (B&R) is a high-end manufacturer of cutting and drilling bits for lathe machines, drill presses, and other metal-working equipment. They pride themselves in producing only bits of the very best quality, guaranteed to last longer than the bits from any of their competitors. Brinell & Rockwell has a hotline where customers can call to report when a B&R bit fails before it is expected. At that time, Brinell & Rockwell will ship a replacement bit to the customer free of charge, and the customer will return the failed bit for examination. Back at the Quality Control Department of Brinell & Rockwell, a team of scientists and engineers - including several with PhDs in Metallurgy - will examine the failed bits under the microscope, X-Ray machines, and other diagnostics equipment to determine exactly what went wrong.

Brinell & Rockwell's quality control team keeps the failed bits that they have collected from customers in large glass containers, using one glass container per bit model. They have gathered thousands of failed drilling and cutting bits of 85 different models, including 57 models of drilling bits. These 57 models of drilling bits can be grouped into four families:

Diamond Bits-12

Tungsten Bits-17

Iridium Bits-23

Adamantium Bits-5

In summary, they have collected failed bits of 85 different models, and they use one glass container for every bit model. Therefore, Brinell & Rockwell has in the lab a total of 85 different glass containers. Taking into account that drilling bits can be grouped into families, we know that 12 glass containers contain Diamond bits, 17 glass containers contain Tungsten bits, 23 glass containers contain Iridium bits, and 5 glass containers contain Adamantium bits.

Part 1

Abe is the first worker to arrive to the lab. Following the standard policy of Brinell & Rockwell, he will pick up the first bit to be inspected from a randomly selected glass container. This means he is equally likely to pick up a bit from any one of the 85 containers.

What is the probability that Abe will pick up an Iridium bit?

Maisie is the second worker to arrive to the lab. Following Brinell & Rockwell policy, she will pick two bits from randomly and independently selected containers. She is equally likely to select any of the containers. Even the container selected to pick up the first bit has the same chance of being chosen as any other container at the time she picks the second bit (meaning that Maisie could grab the same model of bit twice).

What is the probability that Maisie will pick up at least one Iridium bit?

A new piece of equipment, a positronic resonance imager (PRI), has been acquired by Brinell & Rockwell. Their chief scientist, Keri, wants to try it on two randomly selected bit models, different from each other. This means once a bit model is picked up to serve as the first bit, the same model cannot be picked up again.

What is the probability that both bits picked up are Tungsten bits? In other words, what is the probability of drawing two Tungsten bit consecutively, if the container from the first drawing was removed before the second drawing?