A.5 What is the probability of picking two aces in succession from a deck of 52

Question

A.5 What is the probability of picking two aces in succession from a deck of 52 cards, if (a) the first card is replaced before the second card is picked, and bf the second card is not replaced? Consider the joint probability of two events A and B both happening, and use this to show that P(BIA) PIAB)-P(B) P(A) where P(A) means the probability of event A regardless of whether event B occurs, and P(BIA) means the probability of event B given event A. Comment briefly on tho interpretation of this formula if A refers to an observed dataset and B refers to a hypothesis about the data. [5

Explanation / Answer

We have given deck of 52 cards

And we have to select 2 aces

a) Probability of selecting 1st ace = total number of ace / total number of cards = 4 / 52

We have to replace 1st card after selection of 2nd card .

So probability of selecting 2nd ac = total number of ace / total number of cards = 4 / 52

So P( sselcting two aces ) = (4/52)*(4/52) = 1/169

b) Probability of selecting 1st ace = total number of ace / total number of cards = 4 / 52

We have not replace 1st card after selection of 2nd card .

So probability of selecting 2nd ac = remining total number of ace / remining total number of cards = 3 / 51

So P( sselcting two aces ) = (4/52)*(3/51) = 1/221

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