A single die is rolled seven times. Find the probability that 2 appears at most twice.
$begingroup$
A single die is rolled seven times. Find the probability that 2 appears at most twice.
here we rolled die in 7 times so $n(s)=6^7$
from here how to processed
probability
asked Nov 27 '18 at 2:53
learnerlearner
1037
$endgroup$
add a comment |
$begingroup$
A single die is rolled seven times. Find the probability that 2 appears at most twice.
here we rolled die in 7 times so $n(s)=6^7$
from here how to processed
probability
asked Nov 27 '18 at 2:53
learnerlearner
1037
$endgroup$
1
$begingroup$
What it means is that out of the 7 times you roll the die, you get 0,1, or 2 two's.
$endgroup$
– Bram28
Nov 27 '18 at 2:55
$begingroup$
"At most twice" means you see "2" on the die 0, 1, or 2 times in those 7 rolls.
$endgroup$
– Eevee Trainer
Nov 27 '18 at 2:55
add a comment |
$begingroup$
A single die is rolled seven times. Find the probability that 2 appears at most twice.
here we rolled die in 7 times so $n(s)=6^7$
from here how to processed
probability
asked Nov 27 '18 at 2:53
learnerlearner
1037
$endgroup$
A single die is rolled seven times. Find the probability that 2 appears at most twice.
here we rolled die in 7 times so $n(s)=6^7$
from here how to processed
probability
probability
asked Nov 27 '18 at 2:53
learnerlearner
1037
asked Nov 27 '18 at 2:53
learnerlearner
1037
edited Nov 27 '18 at 3:03
learner
asked Nov 27 '18 at 2:53
learnerlearner
1037
asked Nov 27 '18 at 2:53
learnerlearner
1037
asked Nov 27 '18 at 2:53
learnerlearner
1037
1037
1
$begingroup$
What it means is that out of the 7 times you roll the die, you get 0,1, or 2 two's.
$endgroup$
– Bram28
Nov 27 '18 at 2:55
$begingroup$
"At most twice" means you see "2" on the die 0, 1, or 2 times in those 7 rolls.
$endgroup$
– Eevee Trainer
Nov 27 '18 at 2:55
add a comment |
1
$begingroup$
What it means is that out of the 7 times you roll the die, you get 0,1, or 2 two's.
$endgroup$
– Bram28
Nov 27 '18 at 2:55
$begingroup$
"At most twice" means you see "2" on the die 0, 1, or 2 times in those 7 rolls.
$endgroup$
– Eevee Trainer
Nov 27 '18 at 2:55
1
1
$begingroup$
What it means is that out of the 7 times you roll the die, you get 0,1, or 2 two's.
$endgroup$
– Bram28
Nov 27 '18 at 2:55
$begingroup$
What it means is that out of the 7 times you roll the die, you get 0,1, or 2 two's.
$endgroup$
– Bram28
Nov 27 '18 at 2:55
$begingroup$
"At most twice" means you see "2" on the die 0, 1, or 2 times in those 7 rolls.
$endgroup$
– Eevee Trainer
Nov 27 '18 at 2:55
$begingroup$
"At most twice" means you see "2" on the die 0, 1, or 2 times in those 7 rolls.
$endgroup$
– Eevee Trainer
Nov 27 '18 at 2:55
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Let $A_0$ be the event that 2 doesn't appear at all, $A_1$ be the event that 2 appears exactly once and $A_2$ be the event that 2 appears exactly twice. The probability you need to calculate is the probability that $A_0cup A_1cup A_2$ occurs. Note that these events are clearly disjoint, so by additivity of the probability measure, we have:
$$mathbb{P}(A_0cup A_1cup A_2)=mathbb{P}(A_0)+mathbb{P}(A_1)+mathbb{P}(A_2)$$
Now it is easy to see that the desired number is $frac{5^7+7cdot 5^6+binom{7}{2}cdot 5^5}{6^7}$.
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
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add a comment |
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$begingroup$
Let $A_0$ be the event that 2 doesn't appear at all, $A_1$ be the event that 2 appears exactly once and $A_2$ be the event that 2 appears exactly twice. The probability you need to calculate is the probability that $A_0cup A_1cup A_2$ occurs. Note that these events are clearly disjoint, so by additivity of the probability measure, we have:
$$mathbb{P}(A_0cup A_1cup A_2)=mathbb{P}(A_0)+mathbb{P}(A_1)+mathbb{P}(A_2)$$
Now it is easy to see that the desired number is $frac{5^7+7cdot 5^6+binom{7}{2}cdot 5^5}{6^7}$.
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
$endgroup$
add a comment |
$begingroup$
Let $A_0$ be the event that 2 doesn't appear at all, $A_1$ be the event that 2 appears exactly once and $A_2$ be the event that 2 appears exactly twice. The probability you need to calculate is the probability that $A_0cup A_1cup A_2$ occurs. Note that these events are clearly disjoint, so by additivity of the probability measure, we have:
$$mathbb{P}(A_0cup A_1cup A_2)=mathbb{P}(A_0)+mathbb{P}(A_1)+mathbb{P}(A_2)$$
Now it is easy to see that the desired number is $frac{5^7+7cdot 5^6+binom{7}{2}cdot 5^5}{6^7}$.
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
$endgroup$
add a comment |
$begingroup$
Let $A_0$ be the event that 2 doesn't appear at all, $A_1$ be the event that 2 appears exactly once and $A_2$ be the event that 2 appears exactly twice. The probability you need to calculate is the probability that $A_0cup A_1cup A_2$ occurs. Note that these events are clearly disjoint, so by additivity of the probability measure, we have:
$$mathbb{P}(A_0cup A_1cup A_2)=mathbb{P}(A_0)+mathbb{P}(A_1)+mathbb{P}(A_2)$$
Now it is easy to see that the desired number is $frac{5^7+7cdot 5^6+binom{7}{2}cdot 5^5}{6^7}$.
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
$endgroup$
Let $A_0$ be the event that 2 doesn't appear at all, $A_1$ be the event that 2 appears exactly once and $A_2$ be the event that 2 appears exactly twice. The probability you need to calculate is the probability that $A_0cup A_1cup A_2$ occurs. Note that these events are clearly disjoint, so by additivity of the probability measure, we have:
$$mathbb{P}(A_0cup A_1cup A_2)=mathbb{P}(A_0)+mathbb{P}(A_1)+mathbb{P}(A_2)$$
Now it is easy to see that the desired number is $frac{5^7+7cdot 5^6+binom{7}{2}cdot 5^5}{6^7}$.
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
edited Nov 27 '18 at 3:14
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
answered Nov 27 '18 at 3:06
Yulia AlexandrYulia Alexandr
596
596
add a comment |
add a comment |
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1
$begingroup$
What it means is that out of the 7 times you roll the die, you get 0,1, or 2 two's.
$endgroup$
– Bram28
Nov 27 '18 at 2:55
$begingroup$
"At most twice" means you see "2" on the die 0, 1, or 2 times in those 7 rolls.
$endgroup$
– Eevee Trainer
Nov 27 '18 at 2:55