Probability of Rolling a 4 on the First Die
Understanding Probability Basics
When two dice are thrown, each die is an independent event. Each die has 6 faces, numbered from 1 to 6. This means the outcome of one die does not influence the outcome of the other. Calculating the probability of independent events helps us better understand chance and randomness in games and real-world scenarios.Calculating Probability with a Single Die
To find the probability that the first die shows a 4, we can use the following formula for probability:P(A) Number of favorable outcomes / Total number of outcomes
For a single six-sided die, there is only 1 favorable outcome (rolling a 4) out of 6 possible outcomes. Therefore, the probability is:P(First die shows 4) 1 / 6
This means the chance of the first die showing a 4 is 1 in 6, or about 16.67%.Considering the Second Die
The question mentions the probability of getting 4 on both dice. For independent events, the probability of both events occurring is the product of the probabilities of each event. Thus, the probability of rolling a 4 on both dice is:P(First die shows 4 and second die shows 4) P(First die shows 4) × P(Second die shows 4) (1/6) × (1/6) 1/36
However, the probability of getting a 4 on at least one die is calculated by considering the complementary events. The probability of not getting a 4 on the first die is 5/6, and the same for the second die. Therefore, the probability of not getting a 4 on either die is (5/6) × (5/6). Subtracting this from 1 gives the probability of getting a 4 on at least one die:P(At least one die shows 4) 1 - ((5/6) × (5/6)) 1 - 25/36 11/36
This means there is a slightly less than 30.56% chance that at least one of the dice will show a 4.