The following example uses a standard 52 card deck of playing cards. If this is

Question

The following example uses a standard 52 card deck of playing cards. If this is not familiar to you, see appendix 1 following this problem.

What is the probability of randomly drawing an Ace? Do this calculation by hand

Starting with a full deck, what is the probability of randomly drawing two Aces in a row without replacing the first card? Do this calculation by hand.

Using the hypergeometric function in excel, calculate the probability of selecting 5 red cards in a row (in 5 tries without replacing). Don’t forget to show excel functions and arguments

What is the probability of selecting exactly 2 red cards in 5 tries without replacing? This can be answered together with part C in a single hypergeometric table like we did in class

Starting again with a full deck, how many red cards in a row would you need to draw out to say that, with 95% confidence, the deck consists of AT LEAST 50% red cards?

Explanation / Answer

(According to Chegg policy, only four questions will be answered. Please post the remaining in another question)

1. Since there are 4 aces and 52 cards in total, the probability of drawing an ace is 4/52 = 1/13.

2. The probability of drawing first ace = 1/13 = 0.077.

After one ace is drawn, there are 3 aces left out of a total of 51 cards. Probability = 3/51 = 1/17.

=> Probability of drawing two successive aces = 1/13 * 1/17 = 0.0045.

3. The arguments for the excel function HYPGEOMDIST are

Sample_s : 5

Number_sample : 5

Population_s : 26

Number_pop : 52

Probability = 0.0253

4. The arguments for the excel function HYPGEOMDIST are

Sample_s : 2

Number_sample : 5

Population_s : 26

Number_pop : 52

Probability = 0.3125

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