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You roll a number cube three consecutive times. What is the probability that you roll an even number the first two times and a 3 the last time?

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Answer:

1/24 = 0.0417 (3 sf) = 4.17% (3 sf)

Step-by-step explanation:

  • Probability is how likely something is to happen
  • The probability of an event happening = (number of ways it can happen) ÷ (total number of outcomes)

With a number cube there are 6 outcomes: 1, 2, 3, 4, 5 or 6

So the probability of rolling any of these 6 numbers is = 1/6

⇒ probability of rolling a 3 = 1/6

The probability of rolling an even number = the probability of rolling a 2 OR a 4 OR a 6 = 1/6 + 1/6 + 1/6 = 3/6

As rolls are independent from any other rolls, the probability of the second and third roll will not be affected by the first or second roll.  

We can calculate the chances of two or more independent events by multiplying the chances.

Therefore, the probability of getting an even number AND an even number AND a 3 = 3/6 x 3/6 x 1/6 = 1/24

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