Maths

[Kumar A C (chaya Kumar)]

Two dice are thrown together. What is the probability of getting a total of at least 6?

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Hi Kumar,

In the future, when posting GMAT questions, it's important to include the 5 answer choices (since the answers can sometimes provide a hint as to how you could answer the question or a 'shortcut' to help you save time).

When it comes to probability, there are only two outcomes: what you WANT to have happen and what you DON'T WANT. The sum of those two fractions always totals 1.... So you can either calculate the probability of what you want OR you can calculate the probability of what you DON'T WANT and subtract that from 1.

Here, we're asked for the probability of getting a sum of AT LEAST 6 on two dice. Since it would be easier to calculate what we DON'T WANT (a sum of 2, 3, 4 or 5), let's do that instead...

Since there are 6 possible outcomes on each die, there are (6)(6) = 36 possible dice rolls

Sum of 2: 1 option
(1) and (1)

Sum of 3: 2 options
(1)and (2)
(2) and (1)

Sum of 4: 3 options
(1) and (3)
(2) and (2)
(3) and (1)

Sum of 5: 4 options
(1) and (4)
(2) and (3)
(3) and (2)
(4) and (1)

Thus, 10/36 are NOT what we want, so 1 - 10/36 = 26/36 = 13/18 is the probability of rolling a sum of at least 6.

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

p(at least 6) = 1 - p(less than 6)

less than 6 = p(exactly 2) + p(exactly 3) + p(exactly 4) + p(exactly 5)

We can get exactly 2 in one way, exactly 3 in two ways, exactly 4 in three ways, and exactly 5 in four ways, so

less than 6 = 1/36 + 2/36 + 3/36 + 4/36 = 10/36 = 5/18

and we want 1 - 5/18, or 13/18

Armed with this, we're off to the casino ... to lose horribly!