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. five are jelly - filled, 9 are lemon - filled, and 10 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 probability of first - donut

The probability of selecting a lemon - filled donut first is the number of lemon - filled donuts divided by the total number of donuts. There are 9 lemon - filled donuts and 24 total donuts, so the probability $P_1=\frac{9}{24}$.

Step2: Calculate probability of second - donut

After eating one lemon - filled donut, there are 23 donuts left. There are 10 custard - filled donuts, so the probability of selecting a custard - filled donut second is $P_2 = \frac{10}{23}$.

Step3: Calculate combined probability

Since these are independent events in sequence, the probability of both events occurring is the product of their individual probabilities. So $P=P_1\times P_2=\frac{9}{24}\times\frac{10}{23}=\frac{9\times10}{24\times23}=\frac{90}{552}=\frac{15}{92}$.

Answer:

$\frac{15}{92}$