+0

# Dice.

0
150
2

A 6-sided fair die is rolled 10 times. What is the probability of a third 6 on the 10th roll? Thank you.

Oct 21, 2018

#1
+5074
+2

$$P[\text{3rd 6 on roll 10}]=P[\text{2 6's in 9 rolls and a 6 on the 10th roll}=\\ \dbinom{9}{2}\left(\dfrac 1 6\right)^2 \left(\dfrac 5 6\right)^7 \cdot \dfrac 1 6 = \dfrac{78125}{1679616}$$

.
Oct 21, 2018

#1
+5074
+2

$$P[\text{3rd 6 on roll 10}]=P[\text{2 6's in 9 rolls and a 6 on the 10th roll}=\\ \dbinom{9}{2}\left(\dfrac 1 6\right)^2 \left(\dfrac 5 6\right)^7 \cdot \dfrac 1 6 = \dfrac{78125}{1679616}$$

Rom Oct 21, 2018
#2
+100807
0

Thanks Rom,

I don't think I would have thought to do that.

Melody  Oct 21, 2018