# 5.(ii)     A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is (ii) $\small 12$

H Harsh Kankaria

The coin and die are tossed together.

The coin can have only 1 or 6 as possible outcomes and the die can have {1,2,3,4,5,6} as poosible outcomes

Sample space, S = {(x,y): x $\dpi{80} \in$ {1,6} and y $\dpi{80} \in$ {1,2,3,4,5,6}}

= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

Number of possible outcomes, n(S) = 12

(ii) Let E be the event having sum of numbers as 12 = {(6, 6)}

$\therefore$ n(E) = 1

$\therefore$ $\dpi{100} P(E) = \frac{n(E)}{n(S)}$  $= \frac{1}{12}$

The required probability of having 12 as sum of numbers is $\dpi{80} \frac{1}{12}$.

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