Name and ID: Probability Challenge#l 1. There are 3 boxes: a box containing 2 go

Question

Name and ID: Probability Challenge#l 1. There are 3 boxes: a box containing 2 gold coins, a box containing 2 silver coins, a box containing 1 gold coin and 1 silver coin. After choosing a box at random and withdrawing one coin at random, and that happening to be a gold coin, what is the probability of the next coin also being a gold coin? 2. Let us make a dea!I wrote three cards: Behind one card is number 10 (f you get it you get plus 10 points in the midterm); behind the two others O, (zero points) You're given the choice of three cards You pick a card, say No. 1, and me (your instructor), who knows what's behind the cards, flips another card, say No. 3, which has O (zero points) behind. Then I tell you, "Do you want to pick card No. 2?" Is it to your advantage to switch your choice? cjustifys

Explanation / Answer

Solution- Let us denote the following events-

A- Picking first box with 2 gold coins

B-Picking second box with two silver coins

C-Picking third box with one gold and one silver coin.

and E1-First Coin comes gold and E2-Second coin comes gold too.

Then the probabilities of the events would be as follows-

P(A) = P(B)=P(C) = 1/3

and P(E2|E1) = P(SInce first coin is gold then it must be from either Box 1 or box3)

= P(E1 and E2) / P(E1)

= (1/3) / ( 1/3+1/3)

= 1/2

Answer

TY!

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