Predicting a Die Roll
Two independent, fair 6 sided dice are rolled. The first die face shows a 3 . The second die rolls under the table, so you can not see its face. The probability that the dice under the table is 3 given that the first dice is 3 can be written as b a , where a and b are positive coprime integers. What is the value of a + b ?
The answer is 7.
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4 solutions
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How a die roll has 6 sides. Soon, this is the total of chances, and 3 is
1
possibility between
6
. Applying in the fraction, we can see:
- -> b a ={ 6 1 }.
- The sum of a and b is = 1 + 6 = 7
The question makes me confused. :/
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How?
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If you are talking about the answer is simple, because the total of possibilities is 6 and 3 is 1 of 6 . Soon, we need to use in the formula : b a , where b = 6 and a = 1 . 6 1 = 1 + 6 = 7
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@Ewerton Cassiano – I already know that the probability stuff. It's the question. English is not my first language. So yeah. :/
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@Adam Zaim – ok, I'm sorry
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@Ewerton Cassiano – If you start a new discussion about the language you will get information of this
how can a die have the seventh side..?
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This isn't a seventh side, because it is only the sum of possibilities with the total , so 1 + 6 = 7
We have 36 ordered-pair combinations for our fair 2-dice sample space. Let A be the event a 3 is rolled on the first die and B be the event a 3 appears on the second die. This conditional probability is just:
P ( A ∣ B ) = P ( A ) P ( A ∩ B ) = 6 / 3 6 1 / 3 6 = 6 1 .
Hence, a = 1 , b = 6 ⇒ a + b = 7 .
First dice shows 3.
Now the possible combinations with other dice hidden are: (3,1) (3,2) (3,3) (3,4) (3,5) (3,6).
Total possibilities = 6.
Possibility we need, i.e. (3,3) = 1.
Probability = 1/6, i.e. a = 1 & b = 6.
did you ever know what a dice is or you do not understand the proble clearly?you know why?the solution is to know whats below the 3 and its 4 3+4=7ok?
firt choice is 3 that is it is constant....so the probability of getting second dice 3 is 1-5/6....that is 1/6 so a+b=1+6=7....ans..