Question

Look at table below. Find these probabilites. A.) Exactly 1 item B.) More than 2 items C.) At least 1 item D.) At most 3 items?

A sales rep who visits customers at home finds she sells 0, 1, 2, 3, or 4 items according to the following frequency distribution.

Items sold Frequency

0 8
1 10
2 3
3 2
4 1

Answer 1

`A=5/12, B=1/8, C=2/3,D=23/24`

Explanation:

I'm going to rewrite the table here:

`(("no. sold", "frequency"),(0,8),(1,10),(2,3),(3,2),(4,1))`

There are a total of `8+10+3+2+1=24` attempts.

A - Sell exactly 1 item

Exactly 1 item was sold 10 times out of the 24 attempts:

`P("sell exactly 1 item")=10/24=5/12`

B - Sell more than 2 items

More than 2 items were sold 3 times (sold three items twice and four items once) out of the 24 attempts:

`P("sell more than 2 items")=3/24=1/8`

C - Sell at least 1 item

We can look at this by either adding up the times we sold 1, 2, 3, and 4 items, or we can take all 24 events and subtract out the times we sold 0 items (that's what I'll do):

`P("sell at least 1 item")=1-P("sell no items")=1-8/24=16/24=2/3`

D - Sell at least most 3 items

We can look at this by either adding up the times we sold 0, 1, 2, or 3 items, or we can take all 24 events and subtract out the times we sold 4 items (that's what I'll do):

`P("sell no more than 3 items")=1-P("sell 4 items")=1-1/24=23/24`