What is the probability of rolling an odd number and spinning "B," given the sample space below?
1 2 3 4 5 6
A A1 A2 A3 A4 A5 A6
B B1 B2 B3 B4 B5 B6
C C1 C2 C3 C4 C5 C6
D D1 D2 D3 D4 D5 D6
1/2
1/6
1/8
1/12
To find the probability of rolling an odd number and spinning "B," we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's find the number of favorable outcomes, which are the outcomes that satisfy both conditions of rolling an odd number and spinning "B."
From the sample space, we can see that the odd numbers are 1, 3, and 5. And the letter "B" appears in B1, B2, B3, B4, B5, and B6. The favorable outcomes where we roll an odd number and spin "B" are B1, B3, and B5, which make a total of 3 outcomes.
Next, let's determine the total number of possible outcomes. From the sample space, we can see that there are a total of 36 outcomes (6 numbers multiplied by 6 letters = 36).
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes = 3 / 36 = 1/12
Therefore, the probability of rolling an odd number and spinning "B" is 1/12.
To find the probability of rolling an odd number and spinning "B," we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the number of favorable outcomes. From the given sample space, we can see that the odd numbers are 1, 3, and 5. And the letter "B" appears on the second row. So the favorable outcomes are B1, B3, and B5.
Next, let's determine the total number of possible outcomes. Since there are 6 numbers on the dice and 6 letters on the spinner, there are 6 x 6 = 36 total outcomes.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
In this case, the number of favorable outcomes is 3 (B1, B3, B5), and the total number of outcomes is 36.
So the probability of rolling an odd number and spinning "B" is:
Probability = 3 / 36 = 1/12
Therefore, the correct answer is 1/12.
There are 18 possible outcomes in the sample space (6 numbers and 3 letters per number), and there are 9 outcomes that are odd numbers and "B": B1, B3, B5, A5B, C5B, and D1B, D3B, D5B, D7B (assuming A, C, and D represent odd numbers). Therefore, the probability of rolling an odd number and spinning "B" is 9/18, which simplifies to 1/2.
Therefore, the answer is 1/2.