Help on probability again please

In summary, the trials of a biology experiment are performed independently, with a 0.13 probability of success and 0.87 probability of failure. The probability distribution of the random variable Y, representing the number of trials up to and including the first success, is given by Pr(Y=y) = 0.87^(y-1)*0.13. The probability of Y being less than 9 is equal to the sum of the geometric distribution from y=1 to y
  • #1
10
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Homework Statement


Trials of a biology experiment are performed, and each trial is independent of the other
trials. Each experiment trial has a 0.13 probability of a success, and 0.87 probability of
failure.
(c) Let Y denote the random variable representing the number of trials up to and including
the first success. Find an expression for the probability distribution of Y ,
then use MATLAB to compute and plot this function for the first 50 possible values.
(d) Let Y be defined as in (c). Find an expression for and use MATLAB to compute
Pr(Y < 9).
(e) Let Y be defined again as in (c). Find a mathematical expression for and compute
(using MATLAB) the probability that Y is less than or equal to 12 given that Y is
greater than 8.


Homework Equations


n/a


The Attempt at a Solution



is part(c) just
Pr(Y=y) = 0.87^(y-1)*0.13

part(d)
Pr(Y<9) = [tex]\sum(0.87^(y-1)*0.13[/tex]

and got no idea for part (e), need help please.
 
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  • #2
It's a geometric distribution, so yes, your answer to (c) is correct.

For part (d) you have to sum from y=1 to y=8.

[tex] P(Y<13|Y>8) = \frac {P(Y<13 \cap Y>8)}{P(Y>8)} = \frac {P(8>Y>13)}{P(Y>8)} [/tex]

[tex]=\frac { \sum^{12}_{y=9} 0.87^{y-1}(0.13)} { \sum^{\infty}_{y=9} 0.87^{y-1}(0.13)} [/tex]
 
  • #3


For part (c), you are correct. The probability distribution for Y is given by Pr(Y=y) = 0.87^(y-1)*0.13, where y represents the number of trials up to and including the first success.

For part (d), you need to sum up the probabilities for y=1 to y=8, since we want to find the probability that Y is less than 9. So the expression would be Pr(Y<9) = \sum_{y=1}^8 (0.87^(y-1)*0.13).

For part (e), we want to find the probability that Y is less than or equal to 12, given that Y is greater than 8. This can be written as Pr(Y<=12 | Y>8). Using conditional probability, we can rewrite this as Pr(Y<=12 and Y>8)/Pr(Y>8). The expression for Pr(Y<=12 and Y>8) can be found by summing up the probabilities for y=9 to y=12, and Pr(Y>8) can be found by summing up the probabilities for y=9 to infinity. So the final expression would be Pr(Y<=12 | Y>8) = (\sum_{y=9}^{12} (0.87^(y-1)*0.13)) / (\sum_{y=9}^{\infty} (0.87^(y-1)*0.13)). You can use MATLAB to compute this value.
 

1. What is probability?

Probability is a measure of the likelihood that an event will occur. It is often represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. How do you calculate probability?

To calculate probability, you divide the number of favorable outcomes by the total number of possible outcomes. This is known as the probability formula: P(A) = number of favorable outcomes / number of possible outcomes.

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. Experimental probability is based on actual data and can vary depending on the sample size and conditions of the experiment.

4. How can I use probability in real life?

Probability is commonly used in fields such as statistics, finance, and science to make predictions and informed decisions. It can also be applied in everyday life, such as in games of chance or when making risk assessments.

5. What are some common misconceptions about probability?

One common misconception is that if an event has not occurred in a long time, it is more likely to happen soon. This is known as the gambler's fallacy and is not true for independent events. Another misconception is that a low probability event is impossible, when in fact it is just less likely to occur.

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