What is the probability oi rolling a total of 7 in two rolls of a standard die if you get an even number of the first roll?
Could someone please help me? Thanks
The question needs to be understood in a slightly different way. It is 'given' that the first roll was an even number. Hence the probability of a 2 is 1/3, for 4 is 1/3 and for 6 it is 1/3
If previous was a 2, a 5 would = 7-> 1/3 * 1/6 = 1/18
If previous was a 4, a 3 would = 7 -> 1/3 * 1/6 = 1/18
If previous was a 6, a 1 would = 7 -> 1/3 * 1/6 = 1/18
Any one of the above possibilities will result in desired outcome. It is an 'OR' situation. Hence add the possibilities to get 3/18 = 1/6
Well, let me do some quick calculations while juggling some probabilities and juggling balls. When rolling a standard die, we have an equal chance of landing on any number, so the probability of rolling an even number is 1/2. Now, let's break it down.
If we roll an even number on the first roll, there are three possible outcomes for the second roll that would give us a total of 7: (1, 6), (3, 4), and (5, 2). Out of the six possible outcomes for the second roll, three of them give us a total of 7.
Since the probability of getting an even number on the first roll is 1/2, we can multiply it by the probability of getting a valid second roll of 3/6 (3 favorable outcomes out of 6 possible outcomes) to get the final probability.
So, grabbing my juggling balls again, the probability of rolling a total of 7 in two rolls of a standard die if you get an even number on the first roll is:
(1/2) * (3/6) = 1/4
In other words, there's a 25% chance you'll roll a 7 with this situation. Now, go roll those dice and watch the numbers dance!
Certainly! To find the probability of rolling a total of 7 in two rolls of a standard die, given that you get an even number on the first roll, we can break down the problem into two steps:
Step 1: Find the probability of getting an even number on the first roll.
A standard die has six sides, and three of them are even numbers (2, 4, and 6). Thus, the probability of rolling an even number on the first roll is 3/6 or 1/2.
Step 2: Find the probability of rolling a total of 7 on the second roll, given that you got an even number on the first roll.
Once you roll an even number on the first roll, there are two scenarios for getting a total of 7 on the second roll: rolling a 1 or 6, or rolling a 6 or 1. Each of these scenarios has a probability of 1/6.
Now, we multiply the probabilities from both steps to calculate the overall probability:
P(total of 7 | even number on first roll) = P(even number on first roll) * P(total of 7 on second roll)
= 1/2 * 1/6
= 1/12
So, the probability of rolling a total of 7 in two rolls of a standard die, given that you get an even number on the first roll, is 1/12.
Even number can be either 2, 4 or 6. There is 1/6 chance for each one.
If previous was a 2, a 5 would = 7 (1/6 * 1/6) = 1/36
If previous was a 4, a 3 would = 7 (1/6 * 1/6) = 1/36
If previous was a 6, a 1 would = 7 (1/6 * 1/6) = 1/36
Either-or probability is found by multiplying the individual probabilities, 3/36.