+0

# 10 6-sided dice are rolled

0
31
1

Ten 6-sided dice are rolled. What is the probability that exactly three of the dice show a 1? Express your answer as a decimal rounded to the nearest thousandth.

thanks!

Guest Sep 6, 2017
Sort:

### 1+0 Answers

#1
+18564
0

Ten 6-sided dice are rolled. What is the probability that exactly three of the dice show a 1?

Express your answer as a decimal rounded to the nearest thousandth.

thanks!

$$\begin{array}{|rcll|} \hline && \binom{10}{3} \times \left(\frac16 \right)^3 \times \left(\frac56 \right)^7 \\\\ &=& \frac{120 \times 5^7 }{6^{10}} \\ \\ &=& \frac{9375000}{60466176} \\ \\ &=& 0.15504535957 \ (15.5 \% ) \\ \hline \end{array}$$

$$\begin{array}{lcll} \text{possibilities: 10 dices, three "1" } &=& \binom{10}{3} \\ \text{probability: 3dices, three "1" } &=& \left(\frac16 \right)^3 \\ \text{probability: 7dices, no "1" } &=& \left(\frac56 \right)^7 \\ \end{array}$$

heureka  Sep 7, 2017

### 22 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details