Probability of Events

Question

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

 

a. Getting a sum of 2 at least once on 4 rolls of a pair of dice.

 

   The probability is 

 

b. Getting at least one 6 on 4 rolls of a die.

 

   The probability is

Answer 1

Probability of getting a sum of a 2 on a single roll of two dice is 1/36

probability of not getting a sum of 2 on a single roll of two dice is 35/36

probability of getting a sum of 2 at least once = 1 - probability of never getting a sum of two

= 1 - 35/36 * 35/36 * 35/36 * 35/36

Probability of getting a 6 on a single roll of a die is 1/6

Probability of not getting a 6 on a single roll of a die is 5/6

probability of getting a 6 at least once = 1 - probability of never getting a six

= 1 - 5/6 * 5/6 * 5/6 * 5/6