Math Snap

STEP 1

1. Spinner $A$ has six equally likely sections: $2, 1, 1, 3, 2, 3$.
2. Spinner $B$ has four equally likely sections: $4, 1, 3, 2$.
3. Probabilities are calculated based on the number of favorable outcomes over the total number of outcomes.

STEP 2

1. Calculate the probability of landing on specific numbers for both spinners.
2. Evaluate each statement based on the calculated probabilities.

STEP 3

Calculate the probability that spinner $A$ lands on 1.
Spinner $A$ has two sections labeled 1 out of six total sections.
$$P(A \text{ lands on } 1) = \frac{2}{6} = \frac{1}{3}$$

STEP 4

Calculate the probability that spinner $B$ lands on 1.
Spinner $B$ has one section labeled 1 out of four total sections.
$$P(B \text{ lands on } 1) = \frac{1}{4}$$

STEP 5

Compare the probabilities for statement (A).
$$\frac{1}{3} \text{ is not twice } \frac{1}{4}$$ Statement (A) is false.

STEP 6

Calculate the probability that spinner $B$ lands on an odd number.
Odd numbers on spinner $B$ are 1 and 3. There are two odd sections out of four.
$$P(B \text{ lands on odd}) = \frac{2}{4} = \frac{1}{2}$$ Statement (B) is true.

STEP 7

Calculate the probability that spinner $A$ lands on 2.
Spinner $A$ has two sections labeled 2 out of six total sections.
$$P(A \text{ lands on } 2) = \frac{2}{6} = \frac{1}{3}$$ Statement (C) is false because $\frac{1}{3} \neq \frac{1}{4}$.

STEP 8

Determine if spinner $A$ is fair.
A fair spinner would have equal probabilities for each section, which is not the case here.
Spinner $A$ is not fair.

Compare the probability of landing on an odd number for both spinners.
Spinner $A$ odd numbers: 1, 1, 3, 3 (4 out of 6 sections).
$$P(A \text{ lands on odd}) = \frac{4}{6} = \frac{2}{3}$$ Spinner $B$ odd numbers: 1, 3 (2 out of 4 sections).
$$P(B \text{ lands on odd}) = \frac{2}{4} = \frac{1}{2}$$ Spinner $A$ and spinner $B$ are not equally likely to land on an odd number.
The true statements are:
- (B) The probability that spinner $B$ lands on an odd number is $\frac{1}{2}$.
- Spinner $A$ is not a fair spinner.