elizabeth brought a box of donuts to share. there are two - dozen (24) donuts in the box, all identical in…

elizabeth brought a box of donuts to share. there are two - dozen (24) donuts in the box, all identical in size, shape, and color. four are jelly - filled, 10 are lemon - filled, and 10 are custard - filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting two jelly - filled donuts in a row.\n(type an integer or a simplified fraction.)

elizabeth brought a box of donuts to share. there are two - dozen (24) donuts in the box, all identical in size, shape, and color. four are jelly - filled, 10 are lemon - filled, and 10 are custard - filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting two jelly - filled donuts in a row.\n(type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Calculate first - pick probability

The probability of selecting a jelly - filled donut on the first pick is the number of jelly - filled donuts divided by the total number of donuts. There are 4 jelly - filled donuts and 24 total donuts. So the probability $P_1=\frac{4}{24}=\frac{1}{6}$.

Step2: Calculate second - pick probability

After eating one jelly - filled donut, there are 3 jelly - filled donuts left and 23 total donuts left. So the probability of selecting a jelly - filled donut on the second pick given that a jelly - filled donut was selected on the first pick is $P_2 = \frac{3}{23}$.

Step3: Calculate joint probability

Since these are independent events (in the sense of sequential selection without replacement), the probability of both events occurring is the product of their probabilities. So $P = P_1\times P_2=\frac{1}{6}\times\frac{3}{23}=\frac{3}{138}=\frac{1}{46}$.

Answer:

$\frac{1}{46}$