GATE Mechanical 2024 | GA | Question: 5

Question

Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as $2,3,5$, and $7$. If thrown, the long dice cannot land on the square faces and has $1 / 4$ probability of landing on any of the four rectangular faces. The label on the top face of the dice is the score of the throw.

If thrown together, what is the probability of getting the sum of the two long dice scores greater than $11$?

• A. $3 / 8$
• B. $1 / 8$
• C. $1 / 16$
• D. $3 / 16$

Answer 1

The Correct Answer is Option B) 1/8 .

We have total 16 possible outcomes  out of which only two are favourable outcomes that is (5,7) , (7,5) .

So , the required probablity is 2/16 which is 1/8.

Comments

@Thadymademe You missed the one favourable outcome which is (7,7).

Answer 2

There are 3 possibilities:

5,7 or 7,5 or 7,7

So the overall probability=3*(1/4)*(1/4)=3/16

Option D)

Answer 3

3/16

Answer 4

Two Dice with 4 faces , Sample space = 4*4 .= 16.

Favourable cases for scores greater than 11 = (5,7) , (7,7) , (7,5). = 3

Hence the answer would be 3/16.