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A die is rolled 12 times. Find the probability of rolling no more than 4 fives.

Guest Feb 21, 2015

Best Answer 

 #2
avatar+93691 
+10

P(no more thatn 4 fours) = P(no fours)+P(1four)+P(2 fours)+P(3 fours)+P(4 fours)

 

$$\\\left(\frac{5}{6}\right)^{12}
\;\;+\;\;^{12}C_1\left(\frac{1}{6}\right)^{1}\left(\frac{5}{6}\right)^{11}
\;\;+\;\;^{12}C_2 \left(\frac{1}{6}\right)^{2}\left(\frac{5}{6}\right)^{10}\\\\
\;\;+\;\;^{12}C_3\left(\frac{1}{6}\right)^{3}\left(\frac{5}{6}\right)^{9}
\;\;+\;\;^{12}C_4\left(\frac{1}{6}\right)^{4}\left(\frac{5}{6}\right)^{8}$$

Melody  Feb 21, 2015
 #1
avatar+90180 
+10

This means we either rolll no fives, one five, two fives, three fives or 4 fives

The probability of rolling no fives is C(12,0)(1/6)^0*(5/6)^12 = 0.1121566547846151

The probability of rolling one five is C(12,1)(1/6)^1*(5/6)^11 = 0.0000000044516784

The probability of rolling two fives is C(12,2)(1/6)^2*(5/6)^10 = 0.2960935686313838

The probability of rolling three fives is C(12,3)(1/6)^3*(5/6)^9 = 0.1973957124209225

The probability of rolling four fives is C(12,4)(1/6)^4*(5/6)^8 = 0.0888280705894151


And summing these we have......about 69.4%  chance of rolling no more than 4 fives

 

CPhill  Feb 21, 2015
 #2
avatar+93691 
+10
Best Answer

P(no more thatn 4 fours) = P(no fours)+P(1four)+P(2 fours)+P(3 fours)+P(4 fours)

 

$$\\\left(\frac{5}{6}\right)^{12}
\;\;+\;\;^{12}C_1\left(\frac{1}{6}\right)^{1}\left(\frac{5}{6}\right)^{11}
\;\;+\;\;^{12}C_2 \left(\frac{1}{6}\right)^{2}\left(\frac{5}{6}\right)^{10}\\\\
\;\;+\;\;^{12}C_3\left(\frac{1}{6}\right)^{3}\left(\frac{5}{6}\right)^{9}
\;\;+\;\;^{12}C_4\left(\frac{1}{6}\right)^{4}\left(\frac{5}{6}\right)^{8}$$

Melody  Feb 21, 2015
 #3
avatar+90180 
+5

I beat you, Melody........!!!!!

 

Boy Sticking His Tongue Out

 

CPhill  Feb 21, 2015
 #4
avatar+93691 
+5

Yes, you beat me fair and square    LOL   :)))

 

AND I DON'T CARE - TAKE THAT !!!

 

Melody  Feb 21, 2015
 #5
avatar+90180 
+5

LMAO......!!!!

 

CPhill  Feb 21, 2015
 #6
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0

what would be the answer to no more than 4 fives in 10 rolls

Guest Jul 11, 2016

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