What is the probability of a security pass being yellow or having a chain?

In summary, the security passes for a certain company come in yellow or white and can have either a clip or a chain. The probability of a pass having a clip is 6/10, with 2/3 of white passes and 4/7 of yellow passes having clips. If a member of the company is stopped on their way to work, the probability of their pass being yellow is unknown. However, the probability of their pass being yellow with a chain is also unknown. If two people are randomly stopped, the probability of one pass being yellow and the other white, with one having a clip and the other a chain, is dependent on the actual number of yellow and white passes and is not specified in the given information.
  • #1
Chewy0087
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Homework Statement


The security passes for a certain company are coloured yellow or white, they're provided with either a clip or a chain. The probability that a pass has a clip is 6/10, 2/3 of the white passes and 4/7 of the yellow ones are fitted with clips. A member of the company is stopped on his way into work find the probability that;

The pass is yellow
The pass is yellow with a chain

If two people are stopped randomly as they enter find the probability that one pass will be yellow and the other white, and one will have a clip and the other a chain.

Homework Equations



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The Attempt at a Solution



Really frustrating question, is this question possible? :/ This is what I've tried, but it's wrong according to the book;

(3/7 * 4/10) + (4/7 * 6/10) = 0.514 (I know this is wrong but I was trying anything)

I just don't see how this is possible because surely it's dependant on the actual number that are white and yellow? Surely if there's 1000 white, and 5 yellow, the probability of a yellow is much different than with different numbers there, and they tell you no-where what to assume...

Any help would be great.
 
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  • #2
Got it, sorry, i always post too early.
 
  • #3


I would approach this question by first clarifying any assumptions that need to be made. For example, we could assume that there is an equal number of yellow and white passes, or we could make assumptions about the total number of passes in circulation. Once these assumptions are made, we can use the given information to calculate the probabilities.

To find the probability of a pass being yellow, we can use the information that 2/3 of the white passes and 4/7 of the yellow passes have clips:

P(yellow) = (4/7 * 2/3) + (4/7 * 1/3) = 8/21 + 4/21 = 12/21 = 4/7

Therefore, the probability of a pass being yellow is 4/7.

To find the probability of a yellow pass having a chain, we can use the information that 4/7 of the yellow passes have chains:

P(yellow with chain) = 4/7

To find the probability of one pass being yellow and the other white, and one having a clip and the other a chain, we can use the information that 2/3 of the white passes and 4/7 of the yellow passes have clips, and 4/7 of the yellow passes have chains:

P(yellow and white with clip and chain) = (4/7 * 2/3 * 4/7) + (4/7 * 1/3 * 4/7) = 8/49 + 4/49 = 12/49

Therefore, the probability of one pass being yellow and the other white, and one having a clip and the other a chain is 12/49.

In summary, the probabilities in this question depend on the assumptions that are made. Clarifying these assumptions is important in order to accurately calculate the probabilities.
 

1. What is probability?

Probability is a measure of the likelihood or chance of a certain event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

2. How is probability calculated?

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It can also be calculated using mathematical formulas and techniques, such as the addition and multiplication rules, depending on the situation.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely to occur. Experimental probability is based on actual observations and data collected from experiments or real-life events.

4. How is probability used in statistics?

Probability is a fundamental concept in statistics and is used to make predictions and draw conclusions about a population based on a sample. It is also used to determine the likelihood of certain events occurring in a given scenario.

5. How can probability be applied in everyday life?

Probability is used in many aspects of everyday life, such as weather forecasting, gambling, insurance, and decision-making. It can also help us understand and interpret data from various sources, such as surveys and polls.

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