Britt rolls a regular six-sided die. Find the theoretical probability of
each event. Express your answer as a fraction in lowest terms.
a) rolling a 6
b) rolling a number greater than 3
c) rolling an 8
d) rolling an even number
HELP!
in each case, P(event) = #successes / #total events
For each throw, there are 6 possible events.
So.
(a) there is only one 6, so P(6) = 1/6
now do the others in like wise. Don't be startled on (c).
Sure, I'll try my best to help you out! Here are the answers to each question:
a) The probability of rolling a 6 is 1/6. Why? Well, a regular six-sided die has 6 possible outcomes, and only 1 of those outcomes is a 6.
b) The probability of rolling a number greater than 3 is 1/2. Again, since a regular six-sided die has 6 possible outcomes, only 3 of those outcomes are greater than 3 (4, 5, and 6).
c) Sorry, but it's impossible to roll an 8 with a regular six-sided die. So the probability of rolling an 8 is 0/6, which can't be simplified any further.
d) The probability of rolling an even number is 1/2. There are 3 even numbers on a regular six-sided die (2, 4, and 6), and since there are a total of 6 possible outcomes, the probability is 3/6, which can be simplified to 1/2.
I hope that helps! If you have any more questions, feel free to ask.
Sure, I can help you with that! Let's go through each event step by step.
a) Rolling a 6:
A regular six-sided die has 6 possible outcomes (numbers 1 through 6).
There is only 1 outcome that satisfies the event "rolling a 6" (rolling a 6).
Therefore, the theoretical probability of rolling a 6 is 1/6.
b) Rolling a number greater than 3:
The numbers greater than 3 on a regular six-sided die are 4, 5, and 6.
There are 3 outcomes that satisfy the event "rolling a number greater than 3".
Therefore, the theoretical probability of rolling a number greater than 3 is 3/6, which simplifies to 1/2.
c) Rolling an 8:
Since a regular six-sided die only has numbers from 1 to 6, it is not possible to roll an 8.
Therefore, the theoretical probability of rolling an 8 is 0.
d) Rolling an even number:
The even numbers on a regular six-sided die are 2, 4, and 6.
There are 3 outcomes that satisfy the event "rolling an even number".
Therefore, the theoretical probability of rolling an even number is 3/6, which simplifies to 1/2.
I hope this helps! Let me know if you have any further questions.
Sure! Let's go through each event one by one and calculate the theoretical probabilities using a six-sided die.
a) Rolling a 6:
To calculate the theoretical probability of rolling a 6, we need to know the total number of equally likely outcomes (in this case, the numbers on the die) and the number of successful outcomes (rolling a 6).
For a six-sided die, the total number of equally likely outcomes is 6 (numbers 1 through 6), and the number of successful outcomes is 1 (rolling a 6).
To calculate the probability, we take the number of successful outcomes divided by the total number of outcomes:
Probability of rolling a 6 = Number of successful outcomes / Total number of outcomes
= 1 / 6
= 1/6
So the theoretical probability of rolling a 6 is 1/6.
b) Rolling a number greater than 3:
To calculate the theoretical probability of rolling a number greater than 3, we need to find the total number of successful outcomes (rolling numbers 4, 5, and 6) and divide it by the total number of outcomes (6).
In this case, the number of successful outcomes is 3 (rolling a 4, 5, or 6), and the total number of outcomes is still 6.
Probability of rolling a number greater than 3 = Number of successful outcomes / Total number of outcomes
= 3 / 6
= 1/2
So the theoretical probability of rolling a number greater than 3 is 1/2.
c) Rolling an 8:
In this case, we cannot roll an 8 on a six-sided die. The number 8 is not within the possible outcomes of rolling a die.
Therefore, the theoretical probability of rolling an 8 is 0 (zero).
d) Rolling an even number:
To calculate the theoretical probability of rolling an even number, we need to find the number of successful outcomes (rolling an even number: 2, 4, or 6) and divide it by the total number of outcomes (6).
The number of successful outcomes is 3 (2, 4, or 6), and the total number of outcomes is 6.
Probability of rolling an even number = Number of successful outcomes / Total number of outcomes
= 3 / 6
= 1/2
So the theoretical probability of rolling an even number is 1/2.
I hope this helps! Let me know if you have any further questions.