Event A you roll the die and it's even
Event B you roll the die and it's less than 5
Roll the die once. What is the probability that Event A will occur given that Event B has alrady occured?
would it be 3/4 = .75 or 75% not sure need help
and,
Roll the die once. what is the probability that Event B will ocurr given that Event A has already occured?
would this be 4/3 =1.33 I do not think this is right. I would appreciate it if someone could help me out on how you figure something like this out.
Thanks
Since the rolls of the die are independent, they do not influence subsequent events. If previous events occur by chance, they do not change the probability of whatever occurs next.
Event A = 3/6 = .5
Event B = 4/6 = .67
To find the probability of one event occurring given that another event has already occurred, we use conditional probability. In this case, we want to find the probability of Event A occurring given that Event B has occurred, and the probability of Event B occurring given that Event A has occurred.
Let's start with the first scenario:
1. Probability of Event A given that Event B has occurred:
To calculate this, we need to find the probability of both Event A and Event B happening together and divide it by the probability of Event B occurring.
The probability of Event A and Event B happening together is the probability of rolling an even number less than 5, which includes the numbers 2 and 4. Out of the possible outcomes (1, 2, 3, 4, 5, 6), only 2 and 4 satisfy both conditions. So, the probability of Event A and Event B is 2/6 or 1/3.
The probability of Event B occurring is the probability of rolling a number less than 5, which includes the numbers 1, 2, 3, and 4. So, the probability of Event B happening is 4/6 or 2/3.
To find the probability of Event A occurring given that Event B has occurred, we divide the probability of both events happening by the probability of Event B:
Probability of Event A given Event B = (Probability of Event A and Event B) / Probability of Event B = (1/3) / (2/3) = 1/2.
Therefore, the probability of Event A occurring given that Event B has occurred is 1/2 or 0.5.
Now, let's move onto the second scenario:
2. Probability of Event B given that Event A has occurred:
Similarly, we need to find the probability of Event A and Event B happening together and divide it by the probability of Event A occurring.
The probability of Event A and Event B happening together is still 1/3, as we determined in the first scenario.
The probability of Event A occurring is the probability of rolling an even number, which includes the numbers 2, 4, and 6. So, the probability of Event A happening is 3/6 or 1/2.
To find the probability of Event B occurring given Event A has occurred, we divide the probability of both events happening by the probability of Event A:
Probability of Event B given Event A = (Probability of Event A and Event B) / Probability of Event A = (1/3) / (1/2) = 2/3.
Therefore, the probability of Event B occurring given that Event A has occurred is 2/3 or approximately 0.67.
In conclusion:
1. Probability of Event A given Event B = 1/2 or 0.5.
2. Probability of Event B given Event A = 2/3 or approximately 0.67.
Since the rolls of the die are independent, they do not influence subsequent events.
Event A = 3/6 = .5
Event B = 4/6 = .67