Question

1.) In rolling a pair of dice, what is the probability of a total of 4 or less?

2.) A blue die and a red die are tossed together. Find the probability that the sum is less than 7, given that the blue die shows a 3.

3.) A fair coin is tossed three times. Find the probability of getting at least two tails, given that the first toss is tails.

Answer 1

1) In rolling a pair of dice, probability of a total of 4 or less is computed here as:

= Number of ways that the total is 2, 3 or 4 / Total number of outcomes here.

Total number of outcomes = 6*6 = 36

Total ways to get 2: 1 + 1
Total ways to get 3: 1 + 2, 2 + 1
Total ways to get 4: 1+ 3, 2 + 2, 3 + 1

Therefore total ways to get <= 4 is 6

Probability = 6/36 = 1/6

Therefore 1/6 is the required probability here.

Q2) Given that the blue dice shows a 3, probability that the sum if less than 7 is computed here as:

= Probability that the other dice has a number less than (7 - 3)

= Probability that the red dice has number less than 4

= (3 / 6)

= 1/2

Therefore 1/2 = 0.5 is the required probability here.

Q3) Probability of getting at least two tails, given that the first toss is tail is computed here as:

= 1 - Probability that both the remaining tosses are heads

= 1 - 0.5*0.5

= 1 - 0.25

= 0.75

Therefore 0.75 is the required probability here.