Question

elizabeth brought a box of donuts to share. there are two - dozen (24) donuts in the box, all identical in size, shape, and color. four are jelly - filled, 9 are lemon - filled, and 11 are custard - filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting a lemon - filled donut followed by a custard - filled donut. (type an integer or a simplified fraction)

Explanation:

Step1: Calculate the probability of selecting a lemon - filled donut first

The total number of donuts \(n = 24\). The number of lemon - filled donuts \(m_1=9\).
The probability of selecting a lemon - filled donut first, \(P_1=\frac{9}{24}=\frac{3}{8}\).
After eating the lemon - filled donut, the number of remaining donuts \(n_2 = 24 - 1=23\).

Step2: Calculate the probability of selecting a custard - filled donut second

The number of custard - filled donuts \(m_2 = 11\).
The probability of selecting a custard - filled donut second, given that a lemon - filled donut was selected first, \(P_2=\frac{11}{23}\).

Step3: Use the multiplication rule for independent events (in the case of dependent events, which this is)

The probability of both events (selecting a lemon - filled donut then a custard - filled donut) is \(P = P_1\times P_2\).
Substitute \(P_1=\frac{3}{8}\) and \(P_2=\frac{11}{23}\) into the formula: \(P=\frac{3\times11}{8\times23}=\frac{33}{184}\).

Answer:

\(\frac{33}{184}\)