# Finding Probability with 10 counters.

A bag contains ten counters of which six are red and four are green. A counter is chosen at random; its colour is noted and it is replaced in the bag. A second is then chosen at random. Find the probability that both counters are red.

How we would start this question ? What would be the sample space ? I have completed the questions with dice and card deck but, this question is different from those questions. Can anyone help me please ?

• What's the probability that the first counter selected is red? – quasi Mar 18 '18 at 11:42
• @quasi that would be 6/10 which is 3/5. – Student28 Mar 18 '18 at 11:45
• So consider the events $\text{RR},\,\text{RG},\,\text{GR},\,\text{GG}$. Can you compute probabilities for each of those $4$ events? – quasi Mar 18 '18 at 11:46
• @quasi Yes. Thank you. I am going to complete it now. – Student28 Mar 18 '18 at 11:51
• You only care about the event $\text{RR}$. I was just suggesting to compute all $4$ probabilities to help understand the experiment (and the associated sample space). – quasi Mar 18 '18 at 11:56

If the counter is put back in the bag, then the probability of picking a red counter on each time is independant from each other, so the probability of having picked a red counter two times is: $\frac{6}{10}\times \frac{6}{10}=36$%.
• The probability of having picked a red counter on the first pick is $6$ (red counters) out of $10$ (number of counters in total).
• The probability of having picked a red counter on the second pick is $5$ (red counters remaining) out of $9$ (number of counters in total remaining).
If the problem is changed like that, the probability of having picked both red counters would be $\frac{6}{10} \times \frac{5}{9}=33.33$%.