I need help with part e. of this problem. 3 Suppose a coin and a dye were tossed

Question

I need help with part e. of this problem.

3 Suppose a coin and a dye were tossed. a. What is the sample space S of this experiment? b. How many elementary events are in S? c. What is the event that the coin toss was tails and the dye toss even? d. What is the probability of the event in part c? e. Consider the random variable X(c, d) =t2d if c = H where c represents the coin toss, and d represents the value of the dye toss. Find the event that X = 6. And find Pr(X = 6). ents the coin toxe.d)-sdirer

Explanation / Answer

Here we are told to do part e)

For each of the 12 combinations in the sample space, the value of X is computed as:

Note that if the coin gives head then the value of X is equal to the dice output and if the value of head is H, then the value of X is 2d that is twice the number on the dice. This condition is used to get the values of X for all the 12 combinations here.

Now the required probability here is computed as:

P(X = 6) = 2/ 12 = 0.1667

Therefore 0.1667 is the required probability here.

S T1 T2 T3 T4 T5 T6 H1 H2 H3 H4 H5 H6 X 1 2 3 4 5 6 2 4 6 8 10 12

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