How Do You Know Which to Use and or or in Probability

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Knowing how to summate the probability of an event or events happening can be a valuable skill when making decisions, whether playing a game or in real life. How you calculate probability changes, even so, depending on the type of event you are looking to occur. For example, you would not calculate your chances of winning the lottery the same style y'all would summate your chances of drawing a total house in a game of poker. Once y'all decide whether the events are independent, conditional, or mutually sectional, calculating their probability is very elementary.

1. 1

   Understand the formula for determining probability. Probability is the likelihood of a random event happening.^[1] It is unremarkably expressed every bit a ratio. The probability of something happening is defined by the ratio ${\displaystyle probability={\frac {number\;of\;favorable\;outcomes}{number\;of\;possible\;outcomes}}}$ , where a favorable effect is the consequence yous are seeking to happen.^[2]

2. two

   Determine the probability of a single event happening. To do this, consummate the probability ratio past determining how many favorable outcomes you lot tin can take, and how many possible outcomes you can accept.^[3]

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1. ane

   Determine whether the ii events are contained. Independent events are ones in which the event of one event does not affect the probability of the other upshot happening.^[4]

   • For case, if you lot are using 2 dice, y'all might desire to know what the probability is that y'all will coil a double three. The chance that you will throw a iii with one dice does not bear upon the chance that you will throw a 3 with the 2nd die, thus the events are contained.

2. ii

   Decide the probability of the first event. To do this, ready up the ratio ${\displaystyle probability={\frac {number\;of\;favorable\;outcomes}{number\;of\;possible\;outcomes}}}$ , where a favorable outcome is the issue you lot are seeking to happen.

   • For instance, if the starting time event is throwing a iii with one dice, the number of favorable outcomes is i, since there is just 1 3 on a die. The number of possible outcomes is six, since a dice has six sides. So, your ratio will look similar this: ${\displaystyle probability={\frac {1}{6}}}$ .

3. 3

   Determine the probability of the second event. To do this, ready the ratio, just like you did for the offset event.

4. 4

   Multiply the probabilities of the individual events. This will give you lot the probability of both events happening.^[5]

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1. one

   Determine whether the ii events are provisional. A conditional issue, as well called a dependent event, is an event that may be affected by the event(s) that come up before.^[6]

   • For example, if you lot are cartoon from a standard deck of cards, you might want to know what the probability is of drawing a eye on the first and 2nd draws. Drawing a centre the beginning time affects the probability of information technology happening again, because once you draw one center, at that place are fewer hearts in the deck, and fewer cards in the deck.

2. two

   Make up one's mind the probability of the starting time result happening. To practice this, set up upwardly the ratio ${\displaystyle probability={\frac {number\;of\;favorable\;outcomes}{number\;of\;possible\;outcomes}}}$ , where a favorable outcome is the event you are seeking to happen.

3. iii

   Make up one's mind the probability of the 2d result happening, given that the first event already happened. ^[seven] To do this, y'all volition need to examine how the first upshot happening will affect the number of favorable and possible outcomes of the second result.

4. 4

   Multiply the probabilities of the individual events. This volition give you the probability of both events happening.^[8]

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1. 1

   Determine whether the two events are mutually exclusive. Mutually exclusive events are events that cannot happen at the same time.^[nine]

   • Mutually exclusive events will exist marked by the conjunction or. (Events that are not mutually exclusive will use the conjunction and.)^[10]
   • For instance, if you are rolling i dice, y'all might want to know the probability of rolling a 3 or a four. Y'all cannot roll a 3 and a 4 with 1 die, then the events are mutually exclusive.

2. 2

   Determine the probability of the get-go event. To do this, set the ratio ${\displaystyle probability={\frac {number\;of\;favorable\;outcomes}{number\;of\;possible\;outcomes}}}$ , where a favorable outcome is the event yous are seeking to happen.

   • For instance, if the first event is throwing a iii with one dice, the number of favorable outcomes is 1, since there is only one three on a dice. The number of possible outcomes is 6, since a die has six sides. So, your ratio will expect like this: ${\displaystyle probability={\frac {1}{6}}}$ .

3. three

   Determine the probability of the second event. To do this, fix the ratio, only like you did for the starting time event.

4. 4

   Add the probabilities of the individual events. This will give you the probability of either upshot happening.

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• Question

  What is the formula for probability?

  

  Mario Banuelos is an Assistant Professor of Mathematics at California Land Academy, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome development, and information science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the Academy of California, Merced. Mario has taught at both the high school and collegiate levels.

  

  Assistant Professor of Mathematics

  Expert Answer

• Question

  How exercise you know when to multiply the fractions and when to add them?

  

  Multiplication of probabilities is for when the outcome requires multiple things to happen. (For example, coil a 1 on the showtime die AND, having done that, whorl a iv on the second die.) The combo event has a probability of (one/six)*(1/half dozen). Improver of probabilities is for when an consequence tin be accomplished in multiple ways that can't both happen. (For example, roll EITHER a 1 OR a four on a dice.) The philharmonic event has a probability of (1/6) + (ane/6).

• Question

  If I tossed ii fair dice. What is the probability of getting 7?

  

  The probability is 1 in 6 (1:half dozen or one/6). There are 36 possible combinations of the dice, and half dozen of them result in a vii. For each of the 6 numbers that tin testify on die A, in that location is i number on die B that volition result in a full of 7, so 6 of the 36 possible combinations will total 7, and 6 of 36 is 1 of vi.

• Question

  Can the probability of a unmarried effect exist greater than one?

  

  No. Probabilities range from 0 to 1, with impossible events having probability 0 and certain events having probability i. If you get a negative probability, or 1 greater than one, consider rechecking your work for errors.

• Question

  Can you explain what a complementary effect is?

  

  Either it happens or it won't. If you have 1 event representing "it happens", then its complementary upshot represents "it won't happen". If 2 events are complements, so their probabilities must add up to i.

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Article Summary X

To understand probability, larn that it refers to the likelihood of an unpredictable event occurring. If you want to calculate the probability of a single event, y'all'll desire to divide the number of favorable outcomes by the number of potential outcomes. For case, if you have 5 blue marbles and ten red marbles in a box and want to know the probability of yous pulling out a blue marble, divide 5 by 15. Since y'all can simplify 5 divided by 15 to ane divided by 3, yous know that there is a i in 3 take chances of you pulling out a blue marble. To notice out how to calculate the probability of multiple events taking place, proceed reading!

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