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You are at a family reunion and the cooler contains ten bottles of soda; four Sprite, three Dr. Pepper, and three Cherry Coke. Three times, you randomly pick up a drink for your grandmother. The first time, you get a Dr. Pepper. The second and third times, you get Cherry Coke. What is the probability of getting Dr. Pepper the fourth time and then an Dr. Pepper the fifth time without replacement?

Respuesta :

MrRoyal

Answer:

[tex]Probability = \frac{18}{1860480}[/tex]

Step-by-step explanation:

Given

Soda = 10

Sprite = 4

Dr. Pepper = 3

Cherry Coke = 3

Required

Determine the probability of picking Dr. pepper the fourth and fifth

First, we need to sum up the number of drinks

[tex]Total = 10 + 4 + 3 + 3[/tex]

[tex]Total = 20[/tex]

First Selection: Dr. Pepper

[tex]P_1= \frac{3}{20}[/tex]

Since its probability without replacement;

At this stage: Dr. Pepper = 2 and Total = 19

Second Selection: Cherry Coke

[tex]P_2= \frac{3}{19}[/tex]

At this stage: Dr. Pepper = 2; Cherry Coke = 2 and Total = 18

Third Selection: Cherry Coke

[tex]P_3= \frac{2}{18}[/tex]

[tex]P_3= \frac{1}{9}[/tex]

At this stage: Dr. Pepper = 2; Cherry Coke = 1 and Total = 17

Fourth Selection: Dr. Pepper

[tex]P_4= \frac{2}{17}[/tex]

At this stage: Dr. Pepper = 1; Cherry Coke = 1 and Total = 16

Fifth Selection: Dr. Pepper

[tex]P_5= \frac{1}{16}[/tex]

Multiply the calculated probabilities, to give the required probability

[tex]Probability = P_1 * P_2 * P_3 * P_4 * P_5[/tex]

[tex]Probability = \frac{3}{20} * \frac{3}{19} * \frac{1}{9} * \frac{2}{17} * \frac{1}{16}[/tex]

[tex]Probability = \frac{3 * 3 * 1 * 2 * 1}{20 * 19 * 18 * 17 * 16}[/tex]

[tex]Probability = \frac{18}{1860480}[/tex]

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