Question

A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of these printers are selected at random to be checked by a technician, what is the probability that exactly 3 of those selected are laser printers? What is the probability that at least 3 inkjet printers are selected?

Answer 1

Answer:

Step-by-step explanation:

Laser Printer = 10

Inkjet Printers = 15

Total Printers = 25

6 Printers can be selected in ²⁵C₆

3 to be exactly laser printers  ¹⁰C₃ * ¹⁵C₃

Probability of exactly 3  laser printers =  ¹⁰C₃ * ¹⁵C₃ / ²⁵C₆

 ¹⁰C₃ = 10 * 9 * 8/ (3 * 2 * 1)= 120

¹⁵C₃ = 455

²⁵C₆ = 177100

P = 120 *455 / 177100   = 0.308

at least 3 inkjet printers are selected

3 inkjet + 4 inkjet + 5 inkjet + 6 inkjet

= (¹⁵C₃* ¹⁰C₃   + ¹⁵C₄* ¹⁰C₂ + ¹⁵C₅* ¹⁰C₁   + ¹⁵C₆* ¹⁰C₀)

= (455*120  + 1365*45  + 3003*10 + 5005*1)

= 54600 + 61425 + 30030 + 5005

= 151060

Probability = 151060/177100 = 0.853