A box contains 10 red, 5 green, and 10 blue marbles. A marble is chosen at random from the box, and it is noted that it is not one of the blue marbles. What is the probability that it is green?

Question

BlackTom AI · Accepted Answer

Start by parsing the scenario: the box contains 10 red, 5 green, and 10 blue marbles, totaling 25 marbles. We are told the marble drawn is not blue, so we are effectively choosing from the non-blue marbles only.

First, determine the relevant sample space given the condition. The non-blue marbles consist of 10 red and 5 green, for a total of 15 marbles. This is the set from which the observed marble could have come.

Next, focus on the event of interest within that restricted sample space: drawing a green marble. There are 5 green marbles available in the non-blue group.

Compute the conditional probability: number of favorable green outcomes (5) divided by the size of the conditional sample space (15). That yields 5/15 = 1/3.

Now evaluate each option:
- Option a: None of these. This would only be true if none of the listed probabilities matched the scenario, but 1/3 is indeed achievable, so this is incorrect.
- Option b: 1/4. This would imply 25% probability, which does not align with the 5 green out of 15 non-blue ratio.
- Option c: 1/5. This would be 20%, also not matching the 5/15 calculation.
- Option d: 3/5. This is 60%, far from the calculated conditional probability.
- Option e: 1/3. This matches the computed conditional probability exactly, since 5 green out of 15 non-blue equals 1/3.

In summary, restricting to non-blue marbles changes the sample space to 15, and within that space the green portion is 5 out of 15, which simplifies to 1/3.

csd3240f25-csd3241f25-meta.sg

A box contains 10 red, 5 green, and 10 blue marbles. A marble is chosen at random from the box, and it is noted that it is not one of the blue marbles. What is the probability that it is green?

查看解析

登录即可查看完整答案

类似问题

Question at position 7 CAEBD

Given that the first die shows a 3, what is the probability that S is an even number?

Given that S is 7, what is the probability that the first die showed 4 dots?

A survey found that 60% of households own a dog (D), 40% own a cat (C), and 20% own both a dog and a cat (D∩C). What is the probability that a randomly selected household owns a dog, given that they own a cat?

A bag contains 5 red balls and 5 blue balls. If you draw two balls without replacement, what is the probability that the second ball is red, given that the first ball was red?

If for two events [math: A] and [math: B] , [math: Pr(A)=920] Pr(A)= \frac{9}{20} , [math: Pr(B)=12] Pr(B)= \frac{1}{2} , and [math: Pr(A∩B)=15] Pr(A\cap B)= \frac{1}{5} , then [math: P(A|B)] is equal to :

Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution: Event Relative Frequency Clear & dry 0.20 Cloudy & dry 0.30 Rain 0.40 Snow 0.10 Supposing next Christmas is dry, determine the probability that it will also be cloudy.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单