Find the probability for the experiment of tossing a six-sided die twice. Put the answer in a/b form.
P(the sum is odd or prime)
I suggest you make a table of sums for 6 rows and 6 columns from the numbers from 1 to 6
Fill in the sums, e.g. the first row and last row would be
2 3 4 5 6 7
....
7 8 9 10 11 12
count up all the odd ones, obviously 18 of them
Remember 2 is a prime number so it must be included as well
All other primes would be odd, and are already counted.
so prob(of your event) = 19/36
To find the probability of getting an odd or prime sum when tossing a six-sided die twice, we need to first determine the sample space and the favorable outcomes.
Step 1: Determine the sample space.
When tossing a six-sided die twice, the sample space consists of all possible outcomes. Each toss has 6 possible outcomes since the die has 6 sides, and there are 6 options for each of the two tosses. Therefore, the total number of outcomes in the sample space is 6 * 6 = 36.
Step 2: Determine the favorable outcomes.
We need to determine the outcomes that result in an odd or prime sum. Let's list them:
- (1, 1) - sum = 2 (not an odd or prime sum)
- (1, 2) - sum = 3 (odd and prime sum)
- (1, 3) - sum = 4 (not an odd or prime sum)
- (1, 4) - sum = 5 (odd and prime sum)
- (1, 5) - sum = 6 (not an odd or prime sum)
- (1, 6) - sum = 7 (odd and prime sum)
- (2, 1) - sum = 3 (odd and prime sum)
- (2, 2) - sum = 4 (not an odd or prime sum)
- (2, 3) - sum = 5 (odd and prime sum)
- (2, 4) - sum = 6 (not an odd or prime sum)
- (2, 5) - sum = 7 (odd and prime sum)
- (2, 6) - sum = 8 (not an odd or prime sum)
- (3, 1) - sum = 4 (not an odd or prime sum)
- (3, 2) - sum = 5 (odd and prime sum)
- (3, 3) - sum = 6 (not an odd or prime sum)
- (3, 4) - sum = 7 (odd and prime sum)
- (3, 5) - sum = 8 (not an odd or prime sum)
- (3, 6) - sum = 9 (not an odd or prime sum)
- (4, 1) - sum = 5 (odd and prime sum)
- (4, 2) - sum = 6 (not an odd or prime sum)
- (4, 3) - sum = 7 (odd and prime sum)
- (4, 4) - sum = 8 (not an odd or prime sum)
- (4, 5) - sum = 9 (not an odd or prime sum)
- (4, 6) - sum = 10 (not an odd or prime sum)
- (5, 1) - sum = 6 (not an odd or prime sum)
- (5, 2) - sum = 7 (odd and prime sum)
- (5, 3) - sum = 8 (not an odd or prime sum)
- (5, 4) - sum = 9 (not an odd or prime sum)
- (5, 5) - sum = 10 (not an odd or prime sum)
- (5, 6) - sum = 11 (odd and prime sum)
- (6, 1) - sum = 7 (odd and prime sum)
- (6, 2) - sum = 8 (not an odd or prime sum)
- (6, 3) - sum = 9 (not an odd or prime sum)
- (6, 4) - sum = 10 (not an odd or prime sum)
- (6, 5) - sum = 11 (odd and prime sum)
- (6, 6) - sum = 12 (not an odd or prime sum)
There are 16 favorable outcomes in which the sum is either odd or prime.
Step 3: Calculate the probability.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes in the sample space:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 16 / 36
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:
Probability = (16 / 4) / (36 / 4)
Probability = 4/9
Therefore, the probability of obtaining an odd or prime sum when tossing a six-sided die twice is 4/9.
To find the probability of the sum being odd or prime when tossing a six-sided die twice, we first need to determine the sample space, which represents all possible outcomes.
The sample space in this case consists of all possible combinations of outcomes when tossing a six-sided die twice, resulting in 6 * 6 = 36 equally likely outcomes.
Next, we need to determine the favorable outcomes. We are interested in the sum being odd or prime. Let's break it down:
1. Sum being odd: There are 3 odd numbers on a six-sided die (1, 3, and 5), so we have 3 * 3 = 9 favorable outcomes when tossing the die twice and aiming for an odd sum.
2. Sum being prime: There are 3 prime numbers on a six-sided die (2, 3, and 5). However, we need to exclude the outcome (2, 2) since the sum would be even. So, we have 8 favorable outcomes when tossing the die twice and aiming for a prime sum.
Since the question asks for the probability in a/b form, we need to express the answer as a fraction. To do this, we divide the number of favorable outcomes by the total number of possible outcomes (sample space).
Total favorable outcomes = 9 + 8 = 17
Total possible outcomes (sample space) = 36
Therefore, the probability of the sum being odd or prime is 17/36.