If the probability of a given event is 24/61, what is the probability of the event not happening?
A. 37/61
B. 39/61
C. 61/122
D. 24/39
Answer (2)
The probability of an event happening is 61 24 .
The probability of the event not happening is 1 − 61 24 .
Calculate the difference: 61 61 − 61 24 = 61 37 .
The probability of the event not happening is 61 37 .
Explanation
Understand the problem and provided data Let's analyze the problem. We are given the probability of an event happening, and we need to find the probability of the event not happening. The probability of an event not happening is simply 1 minus the probability of the event happening.
Define the probabilities Let P ( A ) be the probability of the event happening. We are given that P ( A ) = 61 24 . The probability of the event not happening, denoted as P ( not A ) , is equal to 1 − P ( A ) .
Calculate the probability of the event not happening Now, we calculate the probability of the event not happening: P ( not A ) = 1 − P ( A ) = 1 − 61 24 To subtract the fraction from 1, we need to express 1 as a fraction with the same denominator, which is 61. So, 1 = 61 61 . Therefore, P ( not A ) = 61 61 − 61 24 = 61 61 − 24 = 61 37
State the final answer The probability of the event not happening is 61 37 .
Examples
Imagine you're playing a game where you have a 24/61 chance of winning. This calculation tells you that you have a 37/61 chance of not winning, which helps you understand your odds and make informed decisions about whether to play again.
The probability of an event not happening can be calculated by subtracting the probability of the event happening from 1. Given that the probability of the event happening is 61 24 , the probability of the event not happening is 61 37 , which corresponds to option A. 37/61.
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