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Pulsified333
 one year ago
involving the sum of the numbers showing on two fair dice.
(1) What is the probability that exactly one die shows a 6 given that the sum of the numbers is 9?
(2) What is the probability that the sum of the numbers is 9 given that exactly one die shows a 6?
(3) What is the probability that the sum of the numbers is 9 given that at least one die shows a 6?
Pulsified333
 one year ago
involving the sum of the numbers showing on two fair dice. (1) What is the probability that exactly one die shows a 6 given that the sum of the numbers is 9? (2) What is the probability that the sum of the numbers is 9 given that exactly one die shows a 6? (3) What is the probability that the sum of the numbers is 9 given that at least one die shows a 6?

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Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1which one are you stuck on? how far did you get?

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0i haven't gotten any yet. lets start with #1 @jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it tells us in #1, that `given that the sum of the numbers is 9` so we know, for a fact, that the two dice add to 9

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what are the ways to add to 9 with 2 dice?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep, what else? can you list ALL of the ways to add to 9?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so put that all together we have 3+6 4+5 5+4 6+3 there are only 4 ways to do this

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1of these 4 ways, how many have exactly one "6" in them?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah 2 3+6 and 6+3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it would be a fraction Probability of exactly one 6, given sum of 9 = (# of sums with 6 in them)/(# of ways to add to 9) = 2/4 = 1/2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1` given that exactly one die shows a 6` so we know die A is 6 or die B is 6 (both cannot be 6 at the same time)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if die A is 6, then what are the possibilities for die B?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1B could also be 1,2,3 basically it could be anything but 6

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if die A is 6, then die B could be 1,2,3,4,5 similarly if die B is 6, then die A could be 1,2,3,4,5

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0but doesn't the sum have to be 9?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1no, the given here is that one die is 6. That's it

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1this dice chart may help

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0ok so die B could be 1,2,3,4,5

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1how many possible outcomes are there if exactly one die is 6?

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0but it says What is the probability that the sum of the numbers is 9

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1we'll get there

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1in the chart I posted, mark the row that has 6 and the column that has 6. But don't mark the cell that has both 6's. How many cells did you highlight?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you should count 5 along the '6' row and 5 along the '6' column so 10 in total

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1how many of those 10, have a sum of 9?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes, 6+3 and 3+6 we have 2 sums that have a sum of 9 out of 10 outcomes so 2/10 = 1/5 is the answer to #2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and for #3, it's almost identical to #2 BUT the key word in #3 is `at least` so it's possible to have both dice be 6

Pulsified333
 one year ago
Best ResponseYou've already chosen the best response.0so is it 1/5? @jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1we have 2 ways to add to 9 (6+3 or 3+6) however, instead of 10 outcomes, we actually have 11. Again, it's possible to have both dice be 6 so it's actually 2/11
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