How do we find the integer corresponding to this probability problem?
$begingroup$
There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?
MY ATTEMPT
Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.
EDIT
This is my try. If we denote by $R$ the event "two red balls have been selected", we get
begin{align*}
mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
end{align*}
I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.
probability problem-solving
asked Jan 8 at 2:45
user1337user1337
48210
$endgroup$
add a comment |
$begingroup$
There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?
MY ATTEMPT
Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.
EDIT
This is my try. If we denote by $R$ the event "two red balls have been selected", we get
begin{align*}
mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
end{align*}
I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.
probability problem-solving
asked Jan 8 at 2:45
user1337user1337
48210
$endgroup$
add a comment |
$begingroup$
There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?
MY ATTEMPT
Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.
EDIT
This is my try. If we denote by $R$ the event "two red balls have been selected", we get
begin{align*}
mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
end{align*}
I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.
probability problem-solving
asked Jan 8 at 2:45
user1337user1337
48210
$endgroup$
There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?
MY ATTEMPT
Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.
EDIT
This is my try. If we denote by $R$ the event "two red balls have been selected", we get
begin{align*}
mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
end{align*}
I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.
probability problem-solving
probability problem-solving
asked Jan 8 at 2:45
user1337user1337
48210
asked Jan 8 at 2:45
user1337user1337
48210
edited Jan 8 at 2:58
user1337
asked Jan 8 at 2:45
user1337user1337
48210
asked Jan 8 at 2:45
user1337user1337
48210
asked Jan 8 at 2:45
user1337user1337
48210
48210
add a comment |
add a comment |
1 Answer
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Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
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$begingroup$
Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
$endgroup$
add a comment |
$begingroup$
Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
$endgroup$
add a comment |
$begingroup$
Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
$endgroup$
Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
answered Jan 8 at 2:48
Adam JamilAdam Jamil
545
545
add a comment |
add a comment |
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