Question

The pie chart to the right shows how adults rate their financial shape. Suppose 4 people are chosen at random from a group of 1100. what is the probability that all four would rate their financial shape as excellent? (make the assumption that the 1100 people are represented by the pie chart)

PIE CHART DATA:
Excellent 7%
Good 44%
Fair 35%
Poor 13%
Other 1%

Answer 1

0.000022304

Explanation:

Total number of people = 1100

Number of people chosen = 4

Excellent percentage is 7% or 0.07

So, number of people rated excellent =
`0.07*1100= 77`

Others who did not choose excellent =
`1100-77=1023`

So, p(randomly choose 4 excellent)=
`((77C4)(1023C0))/(1100C4)`

=
`(77C4)/(1100C4)`

=
`1353275/60671970975` =
`2.2304e^(-5)`

= 0.000022304

Or second and easy method is simply multiplying:

`(77)/(1100) *(76)/(1099) *(75)/(1098) *(74)/(1097)`

=
`32478600/1456127303400` = 0.000022304