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A pair of dice are tossed. What is the probability that doubles are rolled, given that the sum on the two dice is less than 4? (Round your answer to three decimal places.)

Sagot :

KitdaAneekidn

Answer:

[tex]\approx 0.333[/tex]

Step-by-step explanation:

Whenever given a probability problem, identify how many possible outcomes there are. In this case, we are looking for the sum of two dice to be less than four. Once we find that, we can figure out how many are doubles.

Solving:

First find all dice-roll options that have a sum of less than 4:

[tex]- ~\text{Sum} = 2: (1,1)\\\\-\text{Sum} = 3: (1,2), (2,1)[/tex]

So there are 3 possible combinations that have a sum less than 4.

Now lets see how many of these are doubles:

[tex]- (1,1)\text{ is the only double}[/tex]

Probability:

[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{3} \][/tex]

Now we just need our answer in 3 decimals:

[tex]\[\frac{1}{3} \approx\boxed{ 0.333}\][/tex]

Therefore, the probability rounded to three decimal places is 0.333.

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