Dependent and Independent Events S
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Tom is playing a board game.
He has rolled a six nine times in a row.
What's the probability that his 10th roll will not be a six?
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Step-by-step explanation:

Hello!

If you consider the 6-sided dice to be balanced, then each result has the same probability of occurrence: P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=

And each time Tom rolls the dice is independent of the other times, this means that you can disregard all previous rolls and calculate the 10nth time as if it is the 1st one.

Be the event A: "Tom rolled the dice for the 10nth time and obtained a 6"

The probability of A occurring will be P(A)= 1/6

On the other hand, the complement of "A" will be : "Tom rolled the dice for the 10nth time and didn't obtain a 6"

This means he could obtain a 1 or a 2 or a 3 or a 4 or a 5

You can calculate the probability pf this event by adding the probability of obtaining each value P()= P(1)+P(2)+P(3)+P(4)+P(5)= 1/6*5= 5/6

Or by subtracting the probability of A to the total probability of the sample space:

P()= 1 - P(A)= 1 - 1/6= 5/6

I hope this helps!

it would be 6xy and -16xy.