Question

A pair of dice is thrown, determine the probability of getting.
(a) a total if 4,
(b). at most a total of 5,
(c )a total not less than 6.

Answer 1

Answer:

(a) 1 / 12

(b) 5 / 18

(c) 13 / 18

Step-by-step explanation:

There are 6² = 36 possible outcomes (distinguishing the dice so that the outcomes are equally likely).

(a)  There are 3 ways to get a total of 4:  1+3, 2+2, 3+1 (remember that the dice are distinguished!).

P(total 4) = (# ways of getting total 4) / 36  = 3 / 36 = 1 / 12

(b) Total 2:  1+1      ... 1 way

    Total 3:  1+2, 2+1     ... 2 ways

    Total 4:  3 ways (see part (a))

    Total 5:  1+4, 2+3, 3+2, 4+1     ... 4 ways

    So # ways of getting total at most 5 is 1+2+3+4 = 10.

P(total at most 5) = 10 / 36 = 5 / 18

(c) P(total not less than 6)

= 1 - P(total at most 5)

= 1 - 5/18

= 18/18 - 5/18

= 13 / 18