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How do you find the probability of a single event with multiple outcomes?

To determine the probability of a single event that has multiple outcomes, you can calculate it by dividing the number of favorable outcomes by the total number of possible outcomes.

In the context of probability, an event refers to an occurrence that can happen and may consist of several outcomes. For instance, consider the action of rolling a six-sided die. In this case, the event is rolling the die, and the possible outcomes are the numbers 11, 22, 33, 44, 55, and 66. To find the probability of a specific outcome, you must first identify how many ways that outcome can occur (the favorable outcomes) and then divide this by the total number of possible outcomes.

Let’s examine the probability of rolling an even number on a six-sided die. The even numbers available on the die are 22, 44, and 66. This means there are 33 favorable outcomes. The total number of possible outcomes when rolling the die is 66, as there are six faces. Therefore, the probability is calculated as the number of favorable outcomes (33) divided by the total number of possible outcomes (66):

P(even number)=36=12P(\text{even number}) = \frac{3}{6} = \frac{1}{2}

Thus, the probability of rolling an even number is 12\frac{1}{2}, or equivalently, 50%50\%.

Another illustrative example is drawing a card from a standard deck of 5252 cards. If you aim to find the probability of drawing a heart, you will note that there are 1313 hearts in the deck. The total number of possible outcomes remains 5252. Consequently, the probability of drawing a heart can be expressed as:

P(heart)=1352=14P(\text{heart}) = \frac{13}{52} = \frac{1}{4}

This simplifies to 14\frac{1}{4}, or 25%25\%.

In summary, the crucial steps to finding probability are to identify both the number of favorable outcomes and the total number of possible outcomes. You then divide the count of favorable outcomes by the total outcomes. This approach is applicable to any event with multiple outcomes, whether it involves rolling dice, drawing cards, or other scenarios.

Answered by: Prof. Michael Lewis
IB Physics Tutor
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