Question

whats the probability of rolling a 1 or 5 but not both on two rolls

Answer 1

The sample space for the roll of two dice is given below. There will be total 36 outcomes because there are 6 possibilies for first roll and 6 possibilites for second roll  So 6 * 6 = 35 will be total outcomes

(1,1) (1,2), (1,3), (1,4), (1,5), (1,6), (2,1) (2,2), (2,3), (2,4), (2,5), (2,6), (3,1) (3,2), (3,3), (3,4), (3,5), (3,6), (4,1) (4,2), (4,3), (4,4), (4,5), (4,6), (5,1) (5,2), (5,3), (5,4), (5,5), (5,6), (6,1) (6,2), (6,3), (6,4), (6,5), (6,6)

The outcomes where 1 or 5 rolled in any of the dice are

(1,1) (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,5), (3,1), (3,5), (4,1), (4,5), (5,1) (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,5)

But we have to exclude the outcomes where both 1 and 5 are present

The outcomes where both 1 and 5 are present = (1,5), (5,1)

So the outcomes where 1 or 5 rolled in any of the dice but not both are

(1,1) (1,2), (1,3), (1,4), (1,6), (2,1), (2,5), (3,1), (3,5), (4,1), (4,5), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,5)

Number of such outcomes = 18

So Probabikity of rolling a 1 or 5 but not both on two rolls = (Number of outcomes where 1 or 5 are rolled ibut not both are / Total Number of outcomes on two rolls)

= 18 / 36

= 1/2

So Probabikity of rolling a 1 or 5 but not both on two rolls = 1/2 = 0.5