Math Problem Statement

subtract 1-P(x)=

Solution

Given that P(X)P(X) is the probability of event XX, you want to calculate:

1P(X)1 - P(X)

From the previous calculation, we found:

P(X)=0.3P(X) = 0.3

So,

1P(X)=10.3=0.71 - P(X) = 1 - 0.3 = 0.7

This result, 1P(X)1 - P(X), is actually the probability of the complementary event, which is the event "not XX". Hence,

1P(X)=P(not X)1 - P(X) = P(\text{not } X)

Therefore:

1P(X)=0.71 - P(X) = 0.7

Would you like to go into more detail on this? Here are some related questions that might help:

  1. What is the relationship between P(X)P(X) and P(not X)P(\text{not } X)?
  2. How do complementary probabilities work in mutually exclusive events?
  3. How would you express the sum of P(X)P(X) and P(not X)P(\text{not } X)?
  4. If you knew P(not X)P(\text{not } X) first, how would you find P(X)P(X)?
  5. How do you interpret 1P(X)1 - P(X) in a real-world context?
  6. What is the significance of P(X)+P(not X)=1P(X) + P(\text{not } X) = 1 in probability theory?
  7. Can you explain why P(not X)=1P(X)P(\text{not } X) = 1 - P(X) must always hold true?
  8. How would the calculation change if P(X)P(X) was dependent on another event?

Tip: Always remember that the sum of the probabilities of an event and its complement equals 1.

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Math Problem Analysis

Mathematical Concepts

Probability theory
Complementary events

Formulas

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Theorems

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Suitable Grade Level

Advanced