Subjects probability

Washroom Education C69A7E

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1. **State the problem:** We want to find the probability that a randomly selected person from the poll has completed some post-secondary education and believes people should be allowed to use the washroom of the gender they identify with. 2. **Given data:** - Probability a person believes people should use the washroom of the gender they identify with: $P(B) = 0.44$ - Probability a person has at most high school education: $P(H) = 0.18$ - Probability a person has some post-secondary education: $P(S) = 1 - P(H) = 0.82$ - Probability a person has at most high school education and believes in washroom use by gender identity: $P(H \cap B) = 0.07$ 3. **Find:** $P(S \cap B)$, the probability a person has some post-secondary education and believes in washroom use by gender identity. 4. **Use the law of total probability for $B$:** $$ P(B) = P(H \cap B) + P(S \cap B) $$ 5. **Rearrange to find $P(S \cap B)$:** $$ P(S \cap B) = P(B) - P(H \cap B) $$ 6. **Substitute the values:** $$ P(S \cap B) = 0.44 - 0.07 = 0.37 $$ 7. **Interpretation:** The probability that a randomly selected person has completed some post-secondary education and believes people should be allowed to use the washroom of the gender they identify with is $0.37$ or 37%.