Probability theory in a Television Store.

Probability Level 3

A television store owner estimates that 45 percent of the customers entering his store will purchase an UHD television set, 15 percent will purchase a OLED television set, and 40 percent will just be browsing.

If 5 customers enter his store on a given day, what is the probability that he will sell exactly 2 UHD sets and 1 OLED set on that day ?


The answer is 0.1458.

Vijay Simha by Vijay Simha , 47, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Arjen Vreugdenhil
Oct 27, 2017

One of the ways this can happen is if

  • customers 1 and 2 a UHD set,

  • customer 3 buys an OLED set,

  • customers 4 and 5 just browse.

The probability of this event is p = ( 0.45 ) 2 ⋅ 0.15 ⋅ ( 0.4 ) 2 = 0.00486. p = (0.45)^2\cdot 0.15\cdot (0.4)^2 = 0.00486.

But the customers may buy or browse in a different order; each of these orderings is equally likely. Therefore we must count the different orderings: N = 5 ! 2 ! ⋅ 1 ! ⋅ 2 ! = 10 ⋅ 3 ⋅ 1 = 30. N = \frac{5!}{2!\cdot 1!\cdot 2!} = 10\cdot 3 \cdot 1 = 30. The combined probability, then, is N p = 30 ⋅ 0.00486 = 0.1458 . Np = 30\cdot 0.00486 = \boxed{0.1458}.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...