Question

We roll a fair die repeatedly until we see the number four appear and then we stop. The outcome of the experiment is the number of rolls.a. Describe a sample space Ohm and a probability measure P to model this situation. b. Calculate the probability that the number four never appears.

Answer 1

Answer:

0

Step-by-step explanation:

given that we roll a fair die repeatedly until we see the number four appear and then we stop.

the number 4 can appear either in I throw, or II throw or .... indefinitely

So X = the no of throws can be from 1 to infinity

This is a discrete distribution countable.

Sample space= {1,2,.....}

b) Prob ( 4 never appears) = Prob (any other number appears in all throws)

= $\frac{5}{6} *\frac{5}{6} *\frac{5}{6} *\frac{5}{6} *...\\=(\frac{5}{6} )^n$

where n is the number of throws

As n tends to infinity, this becomes 0 because 5/6 is less than 1.

Hence this probability is approximately 0

Or definitely 4 will appear atleast once.