Answer:
[tex]\frac{1}{6561}[/tex]
Step-by-step explanation:
Probability refers to occurrence of some event.
If two events are independent of each other, that is, when the outcome of one event does not affect the outcome of the other event then find their probability of occurring together by multiplying their independent probabilities.
We know that when a pair of dice is rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6.
Total number of outcomes =36
Favourable outcomes are [tex]\left \{ (1,4),(4,1),(2,3),(3,2)\right \}[/tex]
Number of outcomes favourable to the event = 4
So, Probability = Number of outcomes favourable to the event /Total number of outcomes = [tex]\frac{4}{36}=\frac{1}{9}[/tex]
Therefore,
probability of getting a sum of 5 every time if a pair of dice is rolled 4 times
= [tex]\left ( \frac{1}{9} \right )^4=\frac{1}{6561}[/tex]
