Can someone help me explain this misconception?
A student asks, “What’s wrong with the argument that the probability of rolling a double 6 in two rolls of a die is because ” Write an explanation of your understanding of the student’s misconception.
Sorry I did not include the fractions.
A student asks, “What’s wrong with the argument that the probability of rolling a double 6 in two rolls of a die is 1/3 because 1/6 + 1/6 = 1/3? ”Write an explanation of your understanding of the student’s misconception.
You have a 1/6 chance of a 6 on each roll, 1/6*1/6=1/36 chance of rolling two in a roll. Making it a very rare chance
The student's misconception is based on a misunderstanding of probability and the concept of independent events.
The argument the student presents suggests that the probability of rolling a double 6 in two rolls of a die is higher because there are more chances for a double 6 to occur. However, this is incorrect.
To explain the misconception, we need to understand some basics of probability. When rolling a fair six-sided die, each individual outcome has an equal chance of occurring, which means that the probability of rolling a 6 on one roll is 1/6.
Now, let's consider the probability of rolling a double 6 in two rolls of the die. To find this probability, we need to multiply the probability of rolling a 6 on the first roll by the probability of rolling a 6 on the second roll. Since the events are independent, the outcome of the first roll does not affect the outcome of the second roll.
So, in this case, the probability of rolling a double 6 can be calculated as (1/6) * (1/6) = 1/36. The student's argument mistakenly assumes that because there are two rolls, the probability should be higher. However, each roll is an independent event, and the overall probability is determined by multiplying the individual probabilities.
To correct this misconception, it is important to emphasize that the number of rolls does not affect the probability of an event occurring. Each roll of the die is an independent event, and the probability is determined by the number of favorable outcomes divided by the total number of possible outcomes.