Question

A die and 2 coins are tossed simultaneously. If a head is given a number 1 and a tail a number 0 and each number on the die represents the number itself. Find the probability of getting a sum greater than 5 .

• A. $\frac{1}{6}$
• B. $\frac{5}{24}$
• C. $\frac{2}{5}$
• D. $\frac{1}{3}$

Answer 1

The correct option is D

$\frac{1}{3}$

Let us find the sample space of the following event.
For each number on the die, there have 4 outcomes: ( H, T), (H, H), (T, H), (T, T). $\Rightarrow$ (1,0) , (1,1) , (0,1) , (0,0)

Therefore in total we have 6 $\times$ 4 = 24 outcomes.

Favourable outcomes where sum > 5 are (4, 1, 1) , (5, 0, 1) , (5, 1, 1) , (5, 1, 0) ,(6, 0, 1) , (6, 1, 0) , (6, 1, 1) , (6, 0, 0)

P(getting a sum > 5) = $\frac{8}{24}$ = $\frac{1}{3}$