Problem 18E

PIN pad shipments. Personal identification number (PIN) pads are devices that connect to point-of-sale electronic cash registers for debit and credit card purchases. Refer to The Nilson Report (Oct. 2008) listing of the volume of PIN pad shipments by manufacturers worldwide, Exercise 2.7 (p. 49). Recall that for the 12 manufacturers listed in the table, a total of 334,039 PIN pads were shipped. Suppose you randomly select one of these PIN pads and identify the manufacturer.

Manufacturer |
Number Shipped (units) |

Bitel |
13,500 |

CyberNet |
16,200 |

Fujian Landi |
119,000 |

Glintt (ParaRede) |
5,990 |

Intelligent |
4,562 |

KwangWoo |
42,000 |

Omron |
20,000 |

Pax Tech. |
10,072 |

ProvencoCadmus |
20,000 |

SZZT Electronics |
67,300 |

Toshiba TEC |
12,415 |

Urmet |
3,000 |

Source: Data from The Nilson Report, No. 912, October 2008 (p. 9).

a. Find the probability that the PIN pad is shipped by either Fujian Landi or SZZT Electronics.

b. Suppose that 1,000 of the PIN pads shipped were found to be defective. Find the probability that the PIN pad selected is one of the defectives.

Solution

Step1 of 3:

Given the 12 manufactures are listed in the given table.

Manufacturer |
Number Shipped (units) |

Bitel |
13,500 |

CyberNet |
16,200 |

Fujian Landi |
119,000 |

Glintt (ParaRede) |
5,990 |

Intelligent |
4,562 |

KwangWoo |
42,000 |

Omron |
20,000 |

Pax Tech. |
10,072 |

ProvencoCadmus |
20,000 |

SZZT Electronics |
67,300 |

Toshiba TEC |
12,415 |

Urmet |
3,000 |

Step2 of 3:

a). We need to find the probability that the PIN pad is shipped by either Fujian Landi or SZZT Electronics.

Let us define events:

B = bitel

C = cybernet

G = glint(pava rede)

I = intelligent

K = K wang woo

O = Omron

PT = Pax Tech

PC = Provenco Cadmus

S = SZZT Electronics

T = Toshiba TEC

U = Urmet

The related probabilities are given below table:

Manufacturer |
Number Shipped (units) |
Probability |

Bitel |
13,500 |
0.041 |

CyberNet |
16,200 |
0.049 |

Fujian Landi |
119,000 |
0.357 |

Glintt (ParaRede) |
5,990 |
0.018 |

Intelligent |
4,562 |
0.014 |

KwangWoo |
42,000 |
0.126 |

Omron |
20,000 |
0.06 |

Pax Tech. |
10,072 |
0.031 |

ProvencoCadmus |
20,000 |
0.06 |

SZZT Electronics |
67,300 |
0.202 |

Toshiba TEC |
12,415 |
0.038 |

Urmet |
3,000 |
0.009 |

Total |
334,039 |

Where,

Probability column is calculated by using the following method:

P(B) =

= 0.041

And,

P(C) =

= 0.049

And so on.

Now,

The probability that the PIN pad is shipped by either Fujian Landi or SZZT Electronics is given by: