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. three are jelly - filled, 4 are lemon - filled, and 17 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 jelly - filled donut.(type an integer or a simplified fraction.)

Explanation:

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

The probability of selecting a lemon - filled donut on the first draw is the number of lemon - filled donuts divided by the total number of donuts.
There are \(n = 24\) donuts in total and \(m_1=4\) lemon - filled donuts. So the probability \(P_1=\frac{4}{24}=\frac{1}{6}\)

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

After eating one lemon - filled donut, there are \(n'=24 - 1=23\) donuts left. There are \(m_2 = 3\) jelly - filled donuts. So the probability \(P_2=\frac{3}{23}\)

Step3: Calculate the combined probability

Since these are two dependent events (the outcome of the first event affects the second event), we use the formula \(P = P_1\times P_2\)
\(P=\frac{1}{6}\times\frac{3}{23}=\frac{1\times3}{6\times23}=\frac{3}{138}=\frac{1}{46}\)

Answer:

\(\frac{1}{46}\)