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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, 5 are lemon-filled, and 15 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 jelly-filled donut.

(Type an integer or a simplified fraction.)

Verified Answer :

MisterZeng

Answer:

5/46

Step-by-step explanation:

So we need to find the probability of selecting a custard-filled donut followed by a jelly-filled donut.

We will first calculate the probability of selecting a custard-filled donut:

  - 24 donuts in total.

  - 15 are custard-filled.

  - So, the probability of selecting a custard-filled donut first is 15/24, which simplifies to 5/8.

Then we will calculate the probability of selecting a jelly-filled donut, after a custard-filled donut has been eaten:

  - After eating one custard-filled donut, there are 23 donuts left.

  - Out of these 23, 4 are jelly-filled.

  - So, the probability of selecting a jelly-filled donut second is 4/23.

Now we will multiply the two probabilities:

  - The combined probability of selecting a custard-filled donut first and then a jelly-filled donut is:

    (5/8) * (4/23) = 20/184.

And lastly, we will simplify the fraction:

  - 20/184 simplifies to 5/46.

Therefore, the probability of selecting a custard-filled donut followed by a jelly-filled donut is 5/46.

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