Where is the mistake in my probability calculation for a 20cm string cut?

Thread starter songoku
Start date Sep 15, 2022
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Cut Probability String

In summary, the probability of the shorter piece being at least 8cm when the string is cut randomly is 0.6 or 60%. The shorter piece is determined by randomly selecting a point along the string and cutting it. The length of the string affects the probability, as the longer the string, the smaller the chance of the shorter piece being at least 8cm. The probability is not the same if the string is cut at any point along its length, as it decreases as the cut point moves closer to the 20cm mark. Cutting the string multiple times does not increase the probability, as each cut is an independent event.

Sep 15, 2022

songoku

Homework Statement: Please see below

Relevant Equations: Continuous Uniform Distribution

I want to ask about part (c). This is what I did:

the length of the shorter piece should be 8 ≤ X < 10 so P (8 ≤ X < 10) = 2 . (1/20) = 1/10

But my teacher said the correct answer is 2/10. Where is my mistake?

Thanks

Last edited by a moderator: Sep 16, 2022

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Sep 15, 2022

hutchphd

Science Advisor

Homework Helper

The shorter piece of string does not necessarilly have the mark on it.

Sep 15, 2022

songoku

I understand. Thank you very much hutchphd

FAQ: Where is the mistake in my probability calculation for a 20cm string cut?

What is the probability of the shorter piece being at least 8cm when the string is cut randomly?

The probability of the shorter piece being at least 8cm when the string is cut randomly is 0.6 or 60%. This can be calculated by dividing the length of the shorter piece by the total length of the string, which is 8cm/20cm = 0.4 or 40%. The remaining 60% represents the probability of the shorter piece being longer than 8cm.

How is the probability affected by the length of the string?

The length of the string does not affect the probability of the shorter piece being at least 8cm. This is because the probability is determined by the relative lengths of the shorter and longer pieces, not the absolute lengths. For example, if the string was 40cm long, the probability would still be 60% as long as the shorter piece is 8cm.

Is the probability affected by the method of cutting the string?

No, the probability is not affected by the method of cutting the string. As long as the string is cut randomly, the probability of the shorter piece being at least 8cm will remain the same. This means that the string can be cut in any direction or with any tool, as long as it is done randomly.

Can the probability be greater than 1?

No, the probability cannot be greater than 1. This is because the probability is a measure of the likelihood of an event occurring, and it cannot exceed 100%. In this case, the probability of the shorter piece being at least 8cm is already at its maximum of 60%, so it cannot be greater than 1.

How can the probability be calculated for a different length of the string?

The probability can be calculated for a different length of the string by using the same formula of dividing the length of the shorter piece by the total length of the string. For example, if the string is 30cm long, the probability of the shorter piece being at least 8cm would be 8cm/30cm = 0.2667 or 26.67%.