Question

Hector will roll two fair, six-sided dice at the same time. Let A = the event that at least one die lands with the number 3 facing up. Let B = the event that the sum of the two dice is less than 5.

1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”? 2. Calculate the probability that at least one die lands with 3 facing up and the sum of the two dice is less than 5. 3. What is the correct set notation for the event that “at least one die lands with 3 facing up if the sum of the two dice is less than 5”? 4. Calculate the probability that at least one die lands with 3 facing up if the sum of the two dice is less than 5. 5. What is the correct set notation for the event that “the sum of the two dice is not less than 5 if at least one die lands with 3 facing up”?

Answer #1

1. The correct set nitation for this event is

2. Now, 2 dice are rolled. Total no of possible combinations is =

In case of , we have only two favourable cases, namely :. {1,3} and {3,1}

So.

3. In probability the cirrect notation for this event is A|B

4.

Now, favourable cases to B is :

{1,1}{1,2}{1,3}{2,1}{2,2}{3,1} , ie 6

Som P[B] = 6/36

So. Required probability =

5. The correct notation for this event is B' | A .

If you have any doubts, let me know in the comment section. Thank you

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