A fair die was thrown three times and the outcome was repeatedly six. If the die is thrown again what is the probability of getting six?

Question

Prepp Team · Accepted Answer

Probability of Six on Next Throw

The core principle to understand here is the concept of independent events in probability.

A fair die has 6 faces, numbered 1 through 6.
Each face has an equal probability of landing face up on any given throw.
Crucially, each throw of the die is an independent event. This means the outcome of previous throws has absolutely no influence on the outcome of the next throw.

The fact that the die landed on six three times in a row does not change the inherent probabilities for the *next* throw.

For a fair die, the probability of rolling any specific number (like a six) is calculated as:

$P(\text{Specific Outcome}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

In this case, for rolling a six:

$P(\text{rolling a 6}) = \frac{1}{6}$

Since the next throw is independent of the previous ones, the probability of getting a six remains the same as it was for the first throw.

Therefore, the probability of getting a six on the next throw is $1/6$.

Prepp Team · Answer

$1/216$

Prepp Team · Answer

$1/1296$

Prepp Team · Answer

1