To find the probability of [tex]\( P(A \text{ or } B) \)[/tex], we need to use the formula for the union of two events, which is given by:
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
We are provided with the following probabilities:
- [tex]\( P(A) = 0.60 \)[/tex]
- [tex]\( P(B) = 0.30 \)[/tex]
- [tex]\( P(A \text{ and } B) = 0.10 \)[/tex]
Now, plug these values into the formula:
[tex]\[ P(A \text{ or } B) = 0.60 + 0.30 - 0.10 \][/tex]
Perform the addition and subtraction step-by-step:
1. Add [tex]\( P(A) \)[/tex] and [tex]\( P(B) \)[/tex]:
[tex]\[ 0.60 + 0.30 = 0.90 \][/tex]
2. Subtract [tex]\( P(A \text{ and } B) \)[/tex]:
[tex]\[ 0.90 - 0.10 = 0.80 \][/tex]
Therefore, the probability [tex]\( P(A \text{ or } B) \)[/tex] is 0.80.
So, the correct answer is:
B. 0.80
