if a die is tossed four times what is the probability of getting one six
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
You are looking for the probability of one 6 and three non-6s.
1/6 * (5/6)^3 = ?
To calculate the probability of getting one six when a die is tossed four times, we need to consider the possible outcomes.
Step 1: Determine the total number of possible outcomes.
When a single die is tossed, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. Since we are tossing the die four times, the total number of possible outcomes would be 6 x 6 x 6 x 6 = 1,296.
Step 2: Determine the number of favorable outcomes.
In this case, we want to calculate the probability of getting one six. This can happen in different ways:
- Getting a six on the first toss, and not getting a six on the remaining tosses.
- Not getting a six on the first toss, getting a six on the second toss, and not getting a six on the remaining tosses.
- Not getting a six on the first two tosses, getting a six on the third toss, and not getting a six on the remaining tosses.
- Not getting a six on the first three tosses, and getting a six on the fourth toss.
Each of these scenarios has a probability of 1/6 x 5/6 x 5/6 x 5/6 = 625/6,561.
Step 3: Calculate the probability.
Now, we need to determine how many scenarios fit these criteria. There are four scenarios, as mentioned above. Therefore, the number of favorable outcomes is 4 x (625/6,561) = 2,500/6,561.
Step 4: Calculate the probability.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. So, the probability of getting one six when a die is tossed four times is (2,500/6,561) / (1,296) ≈ 0.192 = 19.2%.