Question

An illustration of a circle with four equal differently colored parts labeled 1, 2, 3, 4 clockwise. An arrow starting at the center points toward 1.

the spinner is spun twice what is the proabability of spinning orange (dots) on both spins? express your answer as a simplified fraction

Answer 1

To find the probability of spinning orange (dots) on both spins, we first need to determine the total number of equally likely outcomes for one spin.

Assuming each of the four colored parts is equally likely, the probability of landing on any one part (including orange) on a single spin is given by:

\[
P(\text{orange}) = \frac{1}{4}
\]

If we define \( P(\text{orange on both spins}) \) as the event of landing on orange in both spins, we can use the multiplication rule for independent events. The probability of two independent events both occurring is the product of their individual probabilities:

\[
P(\text{orange on both spins}) = P(\text{orange on first spin}) \times P(\text{orange on second spin})
\]

Substituting in the probabilities:

\[
P(\text{orange on both spins}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}
\]

Thus, the probability of spinning orange on both spins is:

\[
\boxed{\frac{1}{16}}
\]