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. two are jelly - filled, 9 are lemon - filled, and 13 are custard - filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting a custard - filled donut followed by a lemon - filled donut. (type an integer or a simplified fraction)

Explanation:

Step1: Probability of first donut (custard)

There are 13 custard - filled donuts out of 24 total. So the probability of selecting a custard - filled donut first, \(P(C_1)=\frac{13}{24}\).

Step2: Probability of second donut (lemon)

After selecting a custard - filled donut, there are now 23 donuts left, and 9 of them are lemon - filled. So the probability of selecting a lemon - filled donut second, given that a custard - filled donut was selected first, \(P(L_2|C_1)=\frac{9}{23}\).

Step3: Multiply the probabilities

Since these are two dependent events, the probability of both events happening (selecting a custard - filled donut followed by a lemon - filled donut) is the product of the two probabilities. So \(P = P(C_1)\times P(L_2|C_1)=\frac{13}{24}\times\frac{9}{23}\).
Simplify the fraction: \(\frac{13\times9}{24\times23}=\frac{13\times3}{8\times23}=\frac{39}{184}\).

Answer:

\(\frac{39}{184}\)