Question

Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times?

Answer 1

Rolling a 4 on the first try has a probability of (1/6). Meaning, it is one event out of the six possible events of the die. Rolling a 4 a second time also has a probability of (1/6), because nothing has changed on the die. Your mistake was that you added these numbers, but in this case you must multiply (you can Google why on this; I don't want to take up way too much space here). So, rolling a number cube twice and getting 4 both times has a probability of (1/6)*(1/6) = (1/36). Roughly, this is 0.0278.

Answer 2

Answer:

Hence, the probability of rolling a 4 exactly 2 times is:

$\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}=\dfrac{5^5}{6^7}$

Step-by-step explanation:

It is given that:

Thuy rolls a number cube 7 times.

so the total outcomes are: 6.

Also it is asked to find the probability of rolling a 4 exactly 2 times.

So it could be done by the method that:

$\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}$

( where $\dfrac{1}{6}$ denotes the probability of rolling a 4 and $\dfrac{5}{6}$ denotes the probability of rolling a number other than 4 ).

Hence, the probability of rolling a 4 exactly 2 times is:

$\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}=\dfrac{5^5}{6^7}$