A box contains 10 balls numbered from 1 to 10 inclusive. If Ann removes a ball at random and replaces it, and then Jane removes a ball at random, what is the probability that both women removed the same ball?

Question

thephysicsman · Answer

@DanJS

3mar · Answer

0.01

thephysicsman · Answer

hey @3mar can you explain that?

sshayer · Answer

$$\frac{ 1 }{ 10 }\times \frac{ 1 }{ 10 }=?$$

thephysicsman · Answer

$$\frac{ 1 }{ 100 }$$

thephysicsman · Answer

it's saying the answer is 1/10

3mar · Answer

Sorry it will be 0.1
Because the probability of the first one is 0.1
and the second will be the same 0.1 as it is the same ball.

3mar · Answer

If you got it, tell me.

thephysicsman · Answer

alright so if one person takes out a ball and puts it back it's 1/10

thephysicsman · Answer

then there are still 10 balls left. I get that part

3mar · Answer

Good.

thephysicsman · Answer

if the other person takes it out it's also 1/10.

but I don't understand is that the probability of selecting the same ball wouldn't that mean 1/10*1/10

3mar · Answer

The second person will choose one ball of the 10 balls, the probability will be 0.1

sshayer · Answer

for each it is 1/10

3mar · Answer

sshayer  is right.

thephysicsman · Answer

maybe i'm over thinking this. @3mar I guess i'm thinking about it as in the probability of selecting the same ball but we wouldn't multiply the probabilities because the women are putting the same ball back.

3mar · Answer

Yes
It is 0.1 for each one, not meaning that 0.1*0.1