Determine the probabilities of the events in the following (Hint: Use complementary events.). Give solution rounded to the nearest hundredth.

Question

Determine the probabilities of the events in the following (Hint: Use complementary events.). Give solution rounded to the nearest hundredth.
 
a. Getting at least one sum of 6 or 11 on 6 rolls of a pair of dice.
 
   The probability is

 
b. Getting a sum of 10 or greater at least once in 3 rolls of a pair of dice.
 
   The probability is

Answer 1

Probability of "at least one" is the same as 1 - Probability of zero

 

It is binomial distribution with p = 5/36 + 2/36 = 7/36, N=6, k=0

 

1 - (6 choose 0)*(7/36)^0*(29/26)^6 = 1 - (29/36)^6 = 0.726742

 

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Part B:

 

  Prob ( no 10s, 11s, 12s)

 

  p=30/36, N=3, k=0

 

1 - ( 3 choose 0)*(30/36)^0*(6/36)^3 =

 

 1 - 1/216 =215/216 > 99%