Question

probability models quiz
geometry b is (bva) 25-26 / probability
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each with 9 equal slices. there are 3 red slices, 3 green
slices, 2 blue slices and 1 yellow slice on each wheel. if
noah spins and lands on a yellow slice on both wheels he
wins, but if he lands on any other color, he loses. this
information was used to create the following area model.
area model of spinner 1 and spinner 2 with various probability fractions
what the probability of noah winning the game?
options: 1/9, 1/4, 1/81, 1/8 (note: last option may have ocr error but retains as is)

Explanation:

Step1: Find probability of yellow on Spinner 1

Each spinner has 9 slices, 1 yellow. So \( P(Y_1) = \frac{1}{9} \).

Step2: Find probability of yellow on Spinner 2

Similarly, \( P(Y_2) = \frac{1}{9} \).

Step3: Calculate winning probability (Y on both)

For independent events, \( P(Y_1 \cap Y_2) = P(Y_1) \times P(Y_2) = \frac{1}{9} \times \frac{1}{9} = \frac{1}{81} \). Alternatively, from the area model, the '?' cell (Y-Y) should be \( \frac{1}{9} \times \frac{1}{9} = \frac{1}{81} \), which matches the option \( \frac{1}{81} \).

Answer:

\(\frac{1}{81}\) (assuming the option with \(\frac{1}{81}\) is one of the choices, e.g., if the options include \(\frac{1}{81}\) as an option, that's the correct one)