What Is the Probability That the Maximum of Two Drawn Balls Is 9?

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In summary, the conversation discusses finding the probability of Z being equal to 9 when two balls are chosen at random with replacement from a bag of numbered balls. The number of possible ways to choose two balls with replacement is 100, and there are 17 possible ways for Z to equal 9. The method used to calculate this probability is the (n+k-1)c(k) formula, but the speaker is unsure if their calculation is correct.
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ParisSpart
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we have numbered balls in a bag from 1 to 10. We put our hand and take one. Let the number of X be the first number of the ball. Replace the ball into the bag again and takes another ball at random. Let the number of Y the number of the second ball.

IF Z =max{X, Y}.

we want to find P(Z=9)


First of all i used the type (n+k-1)c(k) because we replace the ball again and i found this (8)c(55) but its says tha its not correct answer, what i am doing wrong?
 
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There are 17 possible ways you choose 2 balls with replacement such that Z=max(X,Y)=9. The number of all possible ways you choose 2 balls with replacement is 100. Now you should be able to find the answer.
 
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FAQ: What Is the Probability That the Maximum of Two Drawn Balls Is 9?

What are numbered balls and replacement?

Numbered balls and replacement is a mathematical concept that involves selecting objects (usually balls) from a set and replacing them back into the set after each selection. Each object is assigned a number, and the selection process is usually random.

How is replacement different from without replacement?

Replacement and without replacement are two methods of selecting objects from a set. In replacement, the object is put back into the set after each selection, while without replacement means that the object is not replaced and cannot be selected again.

What is the purpose of using numbered balls and replacement?

Numbered balls and replacement are used in statistics and probability to simulate real-life scenarios and make predictions. It is also used in experiments and simulations to observe patterns and outcomes.

Can the same numbered ball be selected multiple times with replacement?

Yes, in replacement, the same numbered ball can be selected multiple times. This is because the object is replaced back into the set after each selection, making it available for selection again.

How do you calculate the probability of selecting a specific numbered ball with replacement?

To calculate the probability of selecting a specific numbered ball with replacement, you need to know the total number of objects in the set and the number of times the selection process will be repeated. The probability is calculated by dividing the number of times the specific ball can be selected by the total number of possible selections.

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