I don't understand this. I don't get exactly what I'm supposed to do with the P(parenthes) thingy or how each question differs from the next.
Theoretical and Experimental Probability: A number cube with the numbers 1 through 6 is rolled. Find the given probability.
1. P(number < 2)
a. 1/6
b. 2/6
c. 4/6
d. 3/6
2. P(number ≥ 3)
a. 4/6
b. 1/6
c. 2/6
d. 5/6
3. P(complement of 4)
a.
b.
c.
d.
there is only one number less than 2, and six possible throws. So,
P(n<2) = 1/6
Similarly,
P(n>=3) = P(n∊{3,4,5,6}) = 4/6 = 2/3
P(n≠4) = 1-P(n=4) = 1 - 1/6 = 5/6
Thank you!
To understand how to answer these questions, we need to first understand the concept of probability. Probability is a measure of how likely an event is to occur. It is expressed as a ratio or a fraction, with the number of favorable outcomes in the numerator and the number of possible outcomes in the denominator.
In this case, you are given a number cube with the numbers 1 through 6. So, the total number of possible outcomes is 6.
Now let's look at question 1: P(number < 2). The symbol "<" means "less than." So, you need to find the probability of rolling a number that is less than 2. In this case, there is only one number that satisfies this condition, which is 1. Therefore, the numerator of the fraction will be 1, and the denominator will be 6 (since there are 6 possible outcomes). So the answer would be 1/6.
For question 2: P(number ≥ 3), the symbol "≥" means "greater than or equal to." So, you need to find the probability of rolling a number that is greater than or equal to 3. In this case, there are four numbers that satisfy this condition, which are 3, 4, 5, and 6. Therefore, the numerator of the fraction will be 4, and the denominator will be 6. So the answer would be 4/6, which can also be simplified to 2/3.
Now, for question 3: P(complement of 4). The complement of an event is the opposite of that event. In this case, it means finding the probability of NOT rolling a 4. Since there are 6 possible outcomes and only 1 of them is a 4, the probability of not rolling a 4 is 5/6. Therefore, the answer to this question would be 5/6.
I hope this explanation helps you understand how to approach these types of probability questions. Remember, the numerator represents the number of favorable outcomes, and the denominator represents the total number of possible outcomes.