Question

Miguel is comparing the probabilities of two spinners.
Select all the true statements.

Spinner A and Spinner B. Spinner A is divided into 8 equal sections labeled 1, 2, 3, 4, 1, 2, 1, and 2. Spinner B is divided into 4 equal sections labeled 1, 2, 3, and 4.
A.


It is twice as likely that pointer A will land on 1 as compared to pointer B.

B.


The probability that pointer B will land on an even number is 12
.

C.


The probability that pointer A will land on 1 is 38
.

D.


Spinner A is a fair spinner.

E.


It is equally likely that pointer A will land on an odd number as compared to pointer B.

Answer 1

True statements: B, C, and E.

Reasoning:
- Spinner A: P(1)=3/8, P(2)=3/8, P(3)=1/8, P(4)=1/8.
- Spinner B: P(1)=P(2)=P(3)=P(4)=1/4.

A. False — P_A(1)=3/8 while P_B(1)=1/4, so A is 1.5 times as likely, not twice.
B. True — P_B(even)=P_B(2 or 4)=1/4+1/4=1/2.
C. True — P_A(1)=3/8.
D. False — Spinner A does not give each number equal probability (1 and 2 are more likely), so it’s not “fair” by outcomes.
E. True — P_A(odd)=P_A(1 or 3)=3/8+1/8=1/2 = P_B(odd).