Question

suppose that each circle is equally likely to be selected. one circle is selected at random. determine the probability indicated.

\\(p(-\mid \text{yellow circle obtained})\\)

Explanation:

Identify the sample space and given condition

Using the Conditional Probability knowledge point

• Total circles shown in the top right: 6 circles.
• The circles are:
• Yellow with a plus sign: 2 circles
• Yellow with a minus sign: 2 circles
• Blue with a plus sign: 2 circles
• Given condition \(E_1\): "yellow circle obtained".
• Number of yellow circles, \(n(E_1) = 4\).

Identify the target event

Using the Conditional Probability knowledge point

• Target event \(E_2\): "minus sign obtained" (indicated by the minus sign in the numerator-like position \(P(-\,|\,\text{yellow circle obtained})\)).
• We need to find the number of circles that are both yellow and have a minus sign: \(n(E_1 \text{ and } E_2)\).
• Looking at the yellow circles, 2 of them have a minus sign: \(n(E_1 \text{ and } E_2) = 2\).

Calculate the conditional probability

Using the Conditional Probability knowledge point

$$ P(-\,|\,\text{yellow circle obtained}) = \frac{n(E_1 \text{ and } E_2)}{n(E_1)} = \frac{2}{4} $$

Simplify the fraction

Using the Fraction Simplification knowledge point

$$ \frac{2}{4} = \frac{1}{2} $$

Answer:

Suppose that each circle is equally likely to be selected. One circle is selected at random. Determine the probability indicated.

\(P(-\,|\,\text{yellow circle obtained}) =\) <blank>\(\frac{1}{2}\)</blank>