# 4. (BH 2.65) A standard deck of cards will be shuffled and then the cards will be turned over one at a time until the rst ace is revealed. Let B be

Hello, I'm working on (C) for the following problem.

Can someone please explain me what is going on here? Thank you.

4. (BH 2.65) A standard deck of cards will be shuffled and then the cards will be turnedover one at a time until the ﬁrst ace is revealed. Let B be the event that the next cardin the deck will also be an ace. (a) Intuitively, how do you think P(B) compares in size with 1/ 13 (the overall proportionof aces in a deck of cards)? Explain your intuition. (Give an intuitive discussion ratherthan a mathematical calculation; the goal here is to describe your intuition explicitly.) (b) Let C,- be the event that the ﬁrst ace is at position j in the deck. Find P(Ble) interms of 3', fully simpliﬁed. @Using the law of total probability, ﬁnd an expression for P(B) as a sum. (The sumcan be left unsimpliﬁed, but it should be something that could easily be computed insoftware such as R that can calculate sums.)

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