# Two fair dice are thrown.How do you find the probability that the sum of the numbers thrown is not less than 6 ?

How do you find it? Very carefully. (probability questions can be difficult in that each one can pose unique challenges)

I'm not sure how else to do this question except by writing it all out. Because the number we are summing to is small, there's less ways they can add to less than 6, than it not happening. Therefore its easier to calculate the probability of this not happening and then subtract that from 1. ie. We want to calculate the probability that the sum of 2 die is less than 6. Which is the same as adds to 5 or less (because we dont want the ones equal to 6).

Its important to remember that if the first dice rolls a 1 and the second dice rolls a 3 this is a different event to if the second dice rolls a 1 and the first dice rolls a 3. This means that for every combination of numbers we come up with it could happen in the opposite way as well, except if the same number comes up twice eg one dice shows a 2 and the other also shows a 2 ((you can skip this by writing out both outcomes separately but these shortcuts will make life easier with longer and more difficult questions))

Then I would systematically list the outcomes I'm after, making sure I don't miss any. Outcomes that can happen in 2 ways : 1&2, 1&3, 1&4, 2&3. Total=4 Outcomes that can happen 1 way : 1&1, 2&2. Total=2

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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