Answer :
Answer: [tex]\dfrac{1}{1296}[/tex]
Step-by-step explanation:
Formula of probability : [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Total number of outcomes for a fair die = 6 (From 1 to 6)
When we roll a die , Favorable outcome of getting six =1
So , The probability of getting a six : P(rolling a six)= [tex]\dfrac{1}{6}[/tex]
Since the events of throwing a fair die again and again are independent events.
So , Probability of rolling four successive 6's with four rolls of a fair die
= P(rolling a six) x P(rolling a six) x P(rolling a six) x P(rolling a six) [If event are independent then probability of all occurring together is the product of their individual probability]
= [tex]\dfrac{1}{6}\times\dfrac{1}{6}\times\dfrac{1}{6}\times\dfrac{1}{6}=\dfrac{1}{1296}[/tex]
∴ Probability of rolling four successive 6's with four rolls of a fair die=[tex]\dfrac{1}{1296}[/tex]