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, 10 are lemon - filled, and 12 are custard - filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting two lemon - filled donuts in a row.
( type an integer or a simplified fraction. )

Explanation:

Step1: Find initial probability of lemon donut

There are 10 lemon - filled donuts out of 24 total. So the probability of first selecting a lemon - filled donut, $P_1=\frac{10}{24}=\frac{5}{12}$.

Step2: Find probability after first selection

After eating one lemon - filled donut, there are 9 lemon - filled donuts left and 23 total donuts left. So the probability of selecting a lemon - filled donut the second time, $P_2=\frac{9}{23}$.

Step3: Find the combined probability

Since the two events are dependent, we multiply the probabilities: $P = P_1\times P_2=\frac{5}{12}\times\frac{9}{23}=\frac{5\times9}{12\times23}=\frac{45}{276}=\frac{15}{92}$.

Answer:

$\frac{15}{92}$