Statistics and Probability Problem Compute the following:- 1. If you are told th

Question

Statistics and Probability Problem

Compute the following:-

1. If you are told that exactly one of the first four cards drawn is Red, what is th probalility that the fifth card drawn is the Ace of Spades?

2. If you are told that exactly two of the first four cards drawn is Red, what is the probalitiy that the fifth card drawn is the Ace of Spades?

3. If you are told that exactly three of the firest four careds drawn is Red, what is the probalitiy that the fifth card drawn is the Ace of Spade?

You are to solve each of these problems in two ways. first, using simulation via the R programming language and second by theorietical calculation. Your should turn in a brief wiritten summary of your theoratical solution as well as a summary of the numberes you got visa simulation (include the calculated probasbiltiy and the munber of trials you used in your simulation).

Also explane the sample function if there is a way to simplify theis code by elimination the cards variable.

Explanation / Answer

in all 3 situation involve dealing out 5 cards .

1- exactly one of the first four cards drawn is Red, what is th probalility that the fifth card drawn is the Ace of Spades

2. If you are told that exactly two of the first four cards drawn is Red, what is the probalitiy that the fifth card drawn is the Ace of Spades?

3. If you are told that exactly three of the firest four careds drawn is Red, what is the probalitiy that the fifth card drawn is the Ace of Spade?

If four cards are dealt, three red and a black, then it is given that it contains exactly one black card. By symmetry that means that it contains exactly three red cards. In either case, it does not effect the probability that the next card is the ace of spades.

Since you are told that there are exactly X number of red cards in the first four, it does alter the probability of the final card being the ace of spades.

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