QuestionMary rolled a cube 40 times. Find the experimental probability of rolling a 4, the theoretical probability, and a true statement.
Studdy Solution
STEP 1
Assumptions1. The total number of rolls is40.
. The outcomes of the rolls are as follows1 was rolled5 times, was rolled9 times,3 was rolled4 times,4 was rolled12 times,5 was rolled5 times, and6 was rolled5 times.
3. The cube is fair, meaning each outcome has an equal chance of occurring.
STEP 2
To find the experimental probability of rolling a4, we divide the number of times4 was rolled by the total number of rolls.
STEP 3
Plug in the given values to calculate the experimental probability of rolling a.
STEP 4
Calculate the experimental probability of rolling a4.
STEP 5
To find the theoretical probability of rolling a4, we divide1 by the total number of possible outcomes (, because a cube has faces).
STEP 6
Plug in the given values to calculate the theoretical probability of rolling a4.
STEP 7
Calculate the theoretical probability of rolling a4.
STEP 8
Now, we need to compare the experimental and theoretical probabilities. In theory, as the number of rolls increases, the experimental probability should get closer to the theoretical probability. However, they may not always be equal due to chance. Therefore, the correct statement is "As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal."
(a) The experimental probability of rolling a4 is0.3.
(b) The theoretical probability of rolling a4 is approximately0.167.
(c) As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
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