if a die is tossed four times what is the probability of getting three odd numbers
To determine the probability of getting three odd numbers when a die is tossed four times, we need to consider the total number of outcomes and the number of favorable outcomes.
First, let's calculate the total number of outcomes when tossing a die four times. Since a die has 6 sides, each throw has 6 possible outcomes. As we are tossing the die four times, the total number of outcomes is 6^4 = 1296.
Next, we need to determine the number of favorable outcomes, which represent the number of ways we can get three odd numbers in four tosses of the die.
To calculate this, let's consider the different scenarios:
Scenario 1: Getting three odd numbers and one even number.
In this scenario, we can choose one of the four tosses to get an even number, and the remaining three tosses will be odd numbers. There are a total of 4 * (3^3) ways for this scenario to occur, as we have 4 choices for the even toss and 3 choices (odd numbers) for the remaining three tosses.
Scenario 2: Getting four odd numbers.
In this scenario, all four tosses yield odd numbers. There is only one way for this scenario to occur.
Therefore, the total number of favorable outcomes is: 4 * (3^3) + 1 = 109.
Now, we can calculate the probability by dividing the favorable outcomes by the total outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
= 109 / 1296
≈ 0.084
Hence, the probability of getting three odd numbers when a die is tossed four times is approximately 0.084 or 8.4%.