If P(E) = 0.6 and P(G) = 0.2, which of the following is an impossible value for P(E ∪G)?

Rationale

0.9 is an impossible value for P(E ∪ G).

The probability of the union of two events, P(E ∪ G), cannot exceed the sum of their individual probabilities. In this case, the maximum possible value for P(E ∪ G) is 0.8, which occurs when events E and G are mutually exclusive.

A (0.6) YOUR ANSWER

This value is possible for P(E ∪ G) because it is less than P(E) which is 0.6. This indicates that the union could simply be equal to the probability of event E occurring without involving event G.

B (0.7) YOUR ANSWER

This is also a possible value for P(E ∪ G) as it is less than the maximum possible sum of P(E) and P(G), which is 0.8. The union could occur with some overlap between events E and G, allowing for a total probability of 0.7.

C (0.8) YOUR ANSWER

P(E ∪ G) can equal 0.8 if events E and G are mutually exclusive. This means that the occurrence of one does not affect the occurrence of the other, allowing their probabilities to be summed directly.

D (0.9) CORRECT

This value is impossible for P(E ∪ G) because it exceeds the maximum sum of P(E) + P(G), which is 0.8. According to the rules of probability, the union of two events cannot exceed the sum of their individual probabilities, making 0.9 an invalid option.

Conclusion

In probability theory, the union of events cannot exceed the total probability derived from their individual probabilities. With P(E) at 0.6 and P(G) at 0.2, the maximum value for P(E ∪ G) is 0.8. Therefore, any value above this limit, such as 0.9, cannot occur, highlighting the fundamental principles of probability management in event analysis.

If P(E) = 0.6 and P(G) = 0.2, which of the following is an impossible value for P(E ∪G)?

0.9 is an impossible value for P(E ∪ G).

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