Question

1. A random experiment consists of throwing a triangular shape with three faces three times. The first face has the number 1, the second face has the number 2 and the third face has the letter A.

1. List the sample space of the random experiment.   
2. Assume the faces are equally likely, what is the probability an outcome of experiment has at least one A?                                                                                                  
3. the letter A is three times likely to occur in a throw than the faces that has the numbers and the faces that has the numbers are equally likely. What is the probability an outcome of the experiment has at least one A?  

Answer 1

i)

The sample space is

S={(111),(112),...(AAA)}

Its a triplet of {(i,j,k);i,j,k=(1,2,A)},It consists of 27 elements.

ii)

Assuming each face has an equal probability. We can count the number of experiments where we have at least one A.

We have coloured the elements where we see A as pink. The number of those elements = 19

So the probability of at least one A in a set is 19/27=0.7037

iii)

If the probability of A is three times that of a number.

Let p be the probability of any number

So Probability of A is 3p

So 3p+p+p=5p

We know total probability =1

5p=1

p=1/5

So probability of at least one A= 1- the probability of no A

The probability of no A=

where p=2/5 for any two numbers to come up.

We have 27 such experiments

So the probability of no A in 27 such experiments is =

The probability of at least one A= 1- 0.064^{27}=0.9999