You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form
The events of rolling an even number and not rolling a 2 are independent events.
The probability of rolling an even number on the first roll is 3/6 or 1/2. (There are three even numbers: 2, 4, and 6, out of a total of six possible numbers on the cube.)
If an even number is rolled on the first roll, there are five possible numbers left for the second roll, since we do not want to roll a 2. Therefore, the probability of not rolling a 2 on the second roll, given that an even number was rolled on the first roll, is 5/6.
The probability of rolling an even number on the first roll and not rolling a 2 on the second roll is:
P(even, then not 2) = P(even) x P(not 2 | even)
P(even, then not 2) = (1/2) x (5/6)
P(even, then not 2) = 5/12
Therefore, the probability of rolling an even number on the first roll and not rolling a 2 on the second roll is 5/12 or approximately 0.42.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
a. The theoretical probability of rolling a 3 on a number cube is 1/6. This is because there is only one 3 on the cube, and there are six possible outcomes when rolling the cube. Therefore, the probability of rolling a 3 is:
P(rolling a 3) = 1/6
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 comes up by the total number of rolls:
Experimental probability of rolling a 3 = Number of times a 3 comes up / Total number of rolls
Experimental probability of rolling a 3 = 67/450
To simplify this fraction, we can divide both the numerator and denominator by the greatest common factor of 67 and 450, which is 1:
Experimental probability of rolling a 3 = 67/450
To find the probability of rolling an even number, then not rolling a 2 with a number cube, we need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Determine the total number of outcomes when rolling a number cube twice.
Since you roll the number cube twice, each roll has six possible outcomes: {1, 2, 3, 4, 5, 6}.
Therefore, the total number of outcomes is 6 * 6 = 36.
2. Determine the number of favorable outcomes.
To find the probability of rolling an even number, then not rolling a 2, we need to consider the following cases:
- The first roll is even (2, 4, or 6) and the second roll is any number except 2.
There are three even numbers {2, 4, 6} and five numbers excluding 2: {1, 3, 4, 5, 6}. So, there are 3 * 5 = 15 favorable outcomes.
3. Calculate the probability as a fraction in simplest form.
The probability is given by the number of favorable outcomes divided by the total number of outcomes.
P(even, then not 2) = 15/36.
Since the fraction 15/36 cannot be simplified any further, the probability is 15/36.