Question

Throwing 2 six sided dice, what is the probability of throwing:

i) a seven on the first roll or double ones on the second

ii) a seven on the first or second roll

iii) a seven on the first or any doubles on the second roll

Answer 1

Considering the dice is unbiased.

The probability of getting each number from 1 to 6 is 1/6.

The probability of getting a seven(i.e. sum of two dice should be 7)=6/36=1/6
The probability of getting double ones =1/36
The probability of getting any doubles=6/36=1/6

i)The probability of throwing a seven on the first roll or double ones on the second is the summation of the probability of getting a seven on the first roll and the probability of getting double ones on the second roll

The required probability of the event =1/6 + 1/36 =7/36=0.1944

ii)The required probability of the event =1/6 + 1/6 =2/6=0.3333

iii)The required probability of the event =1/6 + 1/6=2/6=0.3333