Question

Find the probabilities of getting three 3's and then a 4 or a 5 in four rolls of a balanced die.

Answer 1

Getting a three, four and five out of a balanced die is \[\frac{3}{6},\frac{4}{6},\frac{5}{6}\] respectfully

Answer 2

no that is not right

Answer 3

rolling 1 or 4 or 5 or any number has the same chance.
What is it? What is the chance of rolling 3?

Answer 4

1/2

Answer 5

Sorry I mean 1/6

Answer 6

Correct!

Answer 7

So in this case it is saying that you roll 4 times. And what is the chance that you will get 3,3,3,4 or 3,3,3,5

Answer 8

These are called independent events. That means that the first rolls result does not effect the second or third or fourth rolls result.

Answer 9

Probability of rolling a 3 in a side sided die is 1/6.
Probabilty of rolling three 3s in a row is \[\frac{1}{6}*\frac{1}{6}*\frac{1}{6}=\frac{1}{6^3}\]
Probabilty of rolling a 4 or a 5 is the combination of the probability of rolling a 4 plus the probability of rolling a 5
\[\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}\]
The probability of rolling a 4 or a 5 after you roll three 3s is
\[\frac{1}{6}*\frac{1}{6}*\frac{1}{6}*\frac{1}{3}=\frac{1}{3*6^3}\]

Answer 10

If two or more events are independent than the probability of both happening at the same time is the multiple of each probability.

Answer 11

Is it clear what 2le wrote? It is correct

Answer 12

Yes, I was able to get up to the second part of his answer, and couldn't figure out the last part but now I understand it. Thank you both.