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, 8 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 jelly - filled donut followed by a custard - filled donut.
(type an integer or a simplified fraction.)

Explanation:

Step1: Calculate probability of first - donut

The probability of selecting a jelly - filled donut first is the number of jelly - filled donuts divided by the total number of donuts. There are 3 jelly - filled donuts and 24 total donuts. So the probability $P_1=\frac{3}{24}$.

Step2: Calculate probability of second - donut

After eating one jelly - filled donut, there are 23 donuts left. There are 13 custard - filled donuts. So the probability of selecting a custard - filled donut second is $P_2 = \frac{13}{23}$.

Step3: Calculate combined probability

Since these are independent events in a sequence, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{3}{24}\times\frac{13}{23}=\frac{3\times13}{24\times23}=\frac{39}{552}=\frac{13}{184}$.

Answer:

$\frac{13}{184}$