What was the probability of the Roosters winning their last game at home?

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In summary, probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. Theoretical probability is based on mathematical calculations, while experimental probability is based on actual observations. To calculate probability, you divide the number of favorable outcomes by the total number of possible outcomes. Probability has various real-world applications, such as in finance, insurance, weather forecasting, and gambling. Conditional probability is the probability of an event occurring given that another event has already occurred.
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The Roosters know that they will win 80% of their home matches and 40% of their away matches. This season’s fixture has the Roosters playing 55% of their games at home. Given that the Roosters won their last game, what was the probability that it was played at home? To find the probability of winning = 0.8x.55+0.4x0.45 = 0.62

To find if it was played at home 'given' a win then = the intersection of the two / 0.62
 
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Yes it is correct.
In this case, the conditional probability can be equated as:
\(\displaystyle \frac{P(winning-at-home)}{P(winning)}\).
 

FAQ: What was the probability of the Roosters winning their last game at home?

What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

What is the difference between theoretical and experimental probability?

Theoretical probability is the expected probability of an event occurring based on mathematical calculations. Experimental probability is based on actual observations and data collected from experiments or real-life situations.

How do you calculate probability?

To calculate probability, you divide the number of favorable outcomes by the total number of possible outcomes. This is known as the probability formula: P(A) = number of favorable outcomes / total number of possible outcomes.

What are some real-world applications of probability?

Probability is used in many fields, such as finance, insurance, weather forecasting, and gambling. It is also used in everyday situations, such as predicting the chances of winning a game or the likelihood of rain.

What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint event (both events occurring) by the probability of the given event.

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