Discrete random variables

[Math1100]

Hi can someone explain to me what I have done wrong I have attached the question and solution

 

[Steven G]

Can you please state what numbers are on the face of each die?

 

[Math1100]

Here is the question with all the values

 

[Steven G]

How did you get the 1/3 in your calculation?

 

[Romsek]

Let's say Tom flips a 2
Using die 1 Avisha has a probability of 2/3 of winning, i.e. by rolling a 3 or a 5.
Using die 2 Avisha has a probability of 1/3 of wining, i.e. by rolling a 4 or a 6.

It should be clear that she wants to use die 1 and wins with probability 2/3.

If Tom flips a 5 Avisha has no chance of winning with die 1 so she must use die 2 and wins with a probability of 1/6, i.e. rolling a 6.

The coin is said to be fair so each of the flips occurs with probability 1/2.

Thus Avisha's probability of winning is 1/2 x 2/3 + 1/2 x 1/6 = 5/12