Question

Roll a cube numbered from 1 to 6 five times in a row. What is the probability that the number 2 will appear in the five tosses given that the number 2 will appear in the first three tosses,

Answer 1

To find the probability of rolling a 2 in the first three tosses and then rolling a 2 in the remaining two tosses, you can use conditional probability.

First, let's find the probability of rolling a 2 in the first three tosses:

- Probability of rolling a 2 in any single toss = 1/6

- Probability of rolling a 2 in the first three tosses = (1/6) * (1/6) * (1/6) = (1/6)^3

Now, you want to find the probability of rolling a 2 in the remaining two tosses given that you've already rolled a 2 in the first three tosses. Since the events are independent (rolling a 2 in one toss doesn't affect the outcome of another toss), the probability of rolling a 2 in the next two tosses is also (1/6)^2.

So, the probability of rolling a 2 in the first three tosses and then rolling a 2 in the remaining two tosses is:

(1/6)^3 * (1/6)^2 = (1/6)^5 = 1/7776

So, the probability of getting a 2 in all five tosses given that you get a 2 in the first three tosses is 1/7776.

Explanation: