Question

When a balanced die is rolled, the probability that a four will appear is 1/6. Which of the following statements is a reasonable conclusion?

a) If I roll a balanced die 6 times, I will get one four.
b) If I roll a balanced die 300 times, I will get fifty fours.
c) If I roll a balanced die 1200 times, I will get approximately 200 fours.
d) None of the above.

Answer 1

When a balanced die is rolled, the probability of rolling a four is 1/6. Over a large number of rolls, we can expect the number of fours to be close to what we would expect based on the probability.

Step-by-step explanation:

When a balanced die is rolled, the probability of rolling a four is 1/6. This means that out of every six rolls, on average, one of them will be a four. So, in a single roll of a balanced die, there is no guarantee that a four will appear. However, over a large number of rolls, we can expect the number of fours to be close to what we would expect based on the probability.

Option (a) states that if a balanced die is rolled 6 times, one of the rolls will be a four. This is a reasonable conclusion, as the probability of rolling a four in a single roll is 1/6, and over 6 rolls, we can expect close to one four.

Options (b) and (c) have larger numbers of rolls, and since the probability of rolling a four in a single roll is 1/6, it is reasonable to expect a proportion of fours close to 1/6 as the number of rolls increases. Therefore, option (c) is a reasonable conclusion.