This conditional probability question has me confused. A worked solution would be much appreciated to help me understand questions of this form. The question is:
A die is rolled until a 3 or 6 appears, otherwise it is rolled four times. Given that a 3 or 6 did not appear in either of the first two rolls, find the probability for that the die was tossed four times.
I don't understand how the die being rolled four times if a 3 or 6 doesnt appear fits into the solution. I have a few more questions like this I can practice on, but would like to properly understand this one before proceeding.
Best Answer
The dice is rolled until a 3 or 6 appears, or until four throws have been made, whichever comes earlier. (The fourth throw can be 3 or 6.) If we have already rolled the dice twice, here are the possibilities:
Since these are probabilities conditional on the dice being rolled twice without a 3 or 6 showing, 2/3 is the answer.