Answer-
If Jill bought three bears, the probability that she got one from each factory is 0.295
Solution-
A plant manufactures a stuffed bear at three different factories.
The first factory manufactures the bear 55% of the time,
So the probability of buying the bear from first factory is,
[tex]P(F_ 1)=\frac{55}{100}[/tex]
The second factory manufactures the bear 80% of the time,
So the probability of buying the bear from second factory is,
[tex]P(F_2)=\frac{80}{100}[/tex]
The third factory manufactures the bear 67% of the time,
So the probability of buying the bear from third factory is,
[tex]P(F_3)=\frac{67}{100}[/tex]
As all the 3 events are independent of each other, so the probability that she got one from each factory,
[tex]=P(F_1\ and\ F_2\ and\ F_3)[/tex]
[tex]=P(F_1)\times P(F_2)\times P(F_3)[/tex]
[tex]=\frac{55}{100}\times \frac{80}{100} \times \frac{67}{100}[/tex]
[tex]=0.55\times 0.80\times 0.67[/tex]
[tex]=0.295[/tex]
