A cabinet has three drawers. In the first drawer there are 3 gold balls. In the second drawer there are 3 silver balls. In the third drawer there are 3 silver balls and 2 gold balls An experiment consists of choosing a drawer, and then choosing a ball inside it. Each drawer is equally likely to be chosen, and within each drawer, each ball is equally likely to be chosen. For example, P(A gold ball is chosen | Drawer 3 is chosen) 2/5 Given that a gold ball is chosen, what is the probability that the drawer with 3 gold balls was selected? Now what if all the balls are numbered from 1-3 based on which drawer they were in, and then taken from the drawers and placed into a large pile of 11 balls? Each ball in this pile is now equally likely to be chosen, unlike in the previous part. Given that a gold ball is chosen, what is the probability that the gold ball came from the drawer with 3 gold balls?

Solution :

Let be the events that the first, second and the third drawers are selected respectively.

Therefore,

Now the G shows that the events that the gold ball is selected, so

By probability, he gold ball is selected is :

Now the required probability is :

                  = 0.71

Now out of 11 balls, 3+2 = 5 balls are gold balls.

Therefore,

The probability that a gold ball and the first drawer is selected is :

Now the required probability is :

56

step-by-step explanation:

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1