Summarize the following:
Once you’ve figured out what these probabilities are, you’ll calculate them separately. Say you wanted to know the probability of rolling a 5 twice consecutively on a 6-sided die. You know that the probability of rolling one five is 1/6, and the probability of rolling another five with the same die is also 1/6. The first outcome doesn’t interfere with the second. If the occurrence of 1 event alters the probability of a second event occurring, you are measuring the probability of dependent events. For example, if you choose 2 cards out of a deck of 52 cards, when you choose the first card, that affects what cards are available when you choose the second card. To calculate the probability for the second of two dependent events, you’ll need to subtract 1 from the possible number of outcomes when calculating the probability of the second event.   Example 1: Consider the event: Two cards are drawn randomly from a deck of cards. What is the likelihood that both cards are clubs? The likelihood that the first card is a club is 13/52, or 1/4. (There are 13 clubs in every deck of cards.) Now, the likelihood that the second card is a club is 12/51, since 1 club will have already been removed. This is because what you do the first time affects the second. If you draw a 3 of clubs and don't put it back, there will be one less club and one less card in the deck (51 instead of 52).   Example 2: A jar contains 4 blue marbles, 5 red marbles, and 11 white marbles. If 3 marbles are drawn from the jar at random, what is the probability that the first marble is red, the second marble is blue, and the third is white? The probability that the first marble is red is 5/20, or 1/4. The probability of the second marble being blue is 4/19, since we have 1 less marble, but not 1 less blue marble. And the probability that the third marble is white is 11/18, because we’ve already chosen 2 marbles. Regardless of whether you’re dealing with independent or dependent events, and whether you’re working with 2, 3, or even 10 total outcomes, you can calculate the total probability by multiplying the events’ separate probabilities by one another. This will give you the probability of multiple events occurring one after another. So, for the scenario; What is the probability of rolling two consecutive fives on a six-sided die? the probability of both independent events is 1/6. This gives us 1/6 x 1/6 = 1/36. You could also express this as 0.027 or 2.7%.   Example 1: Two cards are drawn randomly from a deck of cards. What is the likelihood that both cards are clubs? The probability of the first event happening is 13/52. The probability of the second event happening is 12/51. The probability is 13/52 x 12/51 = 12/204 = 1/17. You could also express this as 0.058 or 5.8%.  Example 2: A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If three marbles are drawn from the jar at random, what is the probability that the first marble is red, the second marble is blue, and the third is white? The probability of the first event is 5/20. The probability of the second event is 4/19. And the probability of the third event is 11/18. The probability is 5/20 x 4/19 x 11/18 = 44/1368 = 0.032. You could also express this as 3.2%.

summary: Deal with each probability separately to calculate independent events. Consider the effect of prior events when calculating probability for dependent events. Multiply the probabilities of each separate event by one another.


Summarize the following:
Hanging shoe shelves are an easy, inexpensive way to organize shoes. They're usually sturdy enough to hold up for years. Make sure you buy enough to house all your shoes. Hanging shoe shelves go over your clothing rod. They come with two Velcro straps. Simply wrap the straps around, and Velcro them down. Sort your shoes by style, placing the fancy ones together and the everyday styles together. Put the ones you wear most often at eye level, so you can grab them more easily.

summary: Buy a hanging shoe shelf. Hang the shelf. Sort your shoes by style. Place your shoes on the shelf.


Summarize the following:
The quality of your ingredients can affect the quality of your cheese sauce. Start with a sharp cheddar cheese, shredded or in a block. If the cheese comes in a block, use a grater to make 2 cups of shredded cheese.  You can substitute cheddar cheese with other cheeses such as Gouda, or Swiss cheese. To spice up the basic sauce, add salsa, hot sauce, beer, or wine for a little extra flavor. In a saucepan over medium heat, slowly heat the butter for your cheese sauce. Keep an eye on the butter as it melts. You don’t want the butter to brown or turn a dark, burnt color, as this will change the flavor of your sauce. Slowly add the flour to the butter, blending evenly with a whisk. Then, add flour and mix until flour is completely blended with butter. Allow the mixture to cook for several minutes, until it just begins to change color slightly.  Be careful not to burn the mixture, as it will make your cheese sauce taste burnt. Slowly pour in the milk, stirring constantly until the mixture gets thick. Try to avoid lumps in the mixture. Pouring the milk slowly and stirring constantly will help you avoid lumps. Add 1 teaspoon salt, pepper, cayenne pepper, or other spices such as dried rosemary or thyme. Get creative and amp up the flavor of your cheese sauce. Start with 1 teaspoon of your chosen spice. You can adjust the sauce to taste once you add in the cheese. Use caution when adding salt. Too much salt is difficult to remove, and many cheeses have a high salt content already. The sauce may also have salt in it already if you used salted butter. Removing the sauce from the heat before you add the shredded cheese will prevent the sauce from separating or curdling. Add the shredded cheese one handful at a time. Stir the sauce with a spoon and allow the cheese to melt each time before adding more cheese. The cheese sauce may harden as it cools, so serve it right away, drizzled over chips, on a baked potato, or over steamed vegetables. It should keep for up to three days. Don’t reheat leftover sauce over high heat, or reboil it. This will cause it to become stringy or separate. Reheat any leftover sauce on low heat, stirring it constantly until it is ready to serve.
summary: Gather your ingredients. Melt 4 tablespoons of butter. Whisk in 4 tablespoons of flour. Add 3 cups of milk. Add 1 teaspoon spices. Remove the sauce from the heat. Stir in the shredded cheese. Serve immediately. Store any leftover sauce in an airtight container in the refrigerator.