A familiar probability question

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In summary, the question asks for the probability that x is bigger than y*z when x, y, and z are randomly selected from the interval [0,1]. The answer is 3/4 and can be solved using a double integral. The area above the surface x=yz represents this probability geometrically as for each value of y and z, the proportion of x > yz is the proportion above the surface. This can be thought of as a volume, rather than a curve.
  • #1
mesarmath
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hi,

i have been studying for GRE subject

and i saw this question but i could not solve it

x , y and z are selected independently and at random from the interval [0,1], then the probability that x is bigger than y*z is ?

the answer is 3/4

but i want to know how? , i guess it should be solved by double integral.

thanks in advance for any help

edit: i just figured out that [itex] \int_{0}^{1} \int_{0}^{1} (1-yz) dy dz = 3/4 [/itex]
but i could not figure out how the area above the curve x=yz represents that probability geometrically ?
 
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  • #2
Hi mesarmath! :smile:
mesarmath said:
… but i could not figure out how the area above the curve x=yz represents that probability geometrically ?

(it ain't a curve, it's a surface :wink:)

Because for each value y and z, the proportion of x > yz is the proportion below the surface, which is yz/1, and the proportion of x > yz is the proportion above the surface, which is (1 - yz)/1.
 
  • #3
tiny-tim said:
Hi mesarmath! :smile:


(it ain't a curve, it's a surface :wink:)

Because for each value y and z, the proportion of x > yz is the proportion below the surface, which is yz/1, and the proportion of x > yz is the proportion above the surface, which is (1 - yz)/1.

thanks

so we were looking for a volume,
curve was the thing that makes me confused

thanks again :)
 

FAQ: A familiar probability question

What is a familiar probability question?

A familiar probability question is a question that involves calculating the likelihood or chance of a certain outcome occurring. These types of questions often involve a known sample space and a set of possible outcomes.

What are some examples of familiar probability questions?

Examples of familiar probability questions include flipping a coin and getting heads or tails, rolling a die and getting a specific number, or drawing a card from a deck and getting a certain suit or value.

How do you calculate the probability in a familiar probability question?

To calculate the probability in a familiar probability question, you must first determine the total number of possible outcomes, known as the sample space. Then, you can find the number of favorable outcomes, or the outcomes that match the desired outcome, and divide it by the total number of possible outcomes.

What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from experiments or observations and may be affected by random chance and other factors.

How can probability be applied in real-world situations?

Probability can be applied in many real-world situations, such as predicting the likelihood of an event occurring, making decisions based on potential outcomes, and analyzing data in fields such as statistics, finance, and science.

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