### Probability Exercise: Drawing MarblesElias has a jar containing 15 black marbles, 8 red marbles, and 9 white marbles. He will perform the following experiment twice:1. Randomly choose a marble from the jar.2. Record its color.3. Replace the marble back into the jar.He will then choose a second marble and record its color.#### Question:What is the probability of choosing a black marble first and then a red marble on the second draw?### Answer Options:- \( \frac{15}{24} \)- \( \frac{9}{128} \)- \( \frac{135}{1024} \)- \( \frac{15}{128} \)To find the correct answer, it is important to note:1. The total number of marbles is \( 15 + 8 + 9 = 32 \).2. The probability of drawing a black marble first is \( \frac{15}{32} \).3. Since the marble is replaced, the second draw also consists of 32 marbles.4. The probability of drawing a red marble next is \( \frac{8}{32} \).Thus, the combined probability:\[ P(\text{Black, then Red}) = P(\text{Black}) \times P(\text{Red}) \]\[ P(\text{Black, then Red}) = \frac{15}{32} \times \frac{8}{32} = \frac{120}{1024} = \frac{15}{128} \]### Final Answer:\[ P(\text{Black, then Red}) = \frac{15}{128} \]Hence, the correct option is:- \( \boxed{\frac{15}{128}} \)

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Description: ### Probability Exercise: Drawing MarblesElias has a jar containing 15 black marbles, 8 red marbles, and 9 white marbles. He will perform the following experiment twice:1. Randomly choose a marble from the jar.2. Record its color.3. Replace the marb

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Math

Geometry

Elias has a jar of 15 black marbles, 8 red marbles, and 9 white marbles. He will randomly choose a marble, record its color, and replace it in the jar. He will then randomly choose a second marble and record its color. 15/24 What is the probability of choosing a black marble and then a red marble? 9/128 135/1024 15/128

Elias has a jar of 15 black marbles, 8 red marbles, and 9 white marbles. He will randomly choose a marble, record its color, and replace it in the jar. He will then randomly choose a second marble and record its color. 15/24 What is the probability of choosing a black marble and then a red marble? 9/128 135/1024 15/128

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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