Question

Se P(A)= 3/5; P(B)= 3/10 e P(ANB)= 4/10, encontre o valor de P(AUB)?​

Answer 1

Explicação passo-a-passo:

$\large \boxed{ \bf \: P(A \: \cup \: B) = P(A) + P(B) - P(A \: \cap \: B) }\\ \\ P(A \: \cup \: B) = \frac{3}{5} + \frac{3}{10} - \frac{4}{10} \\ \\ P(A \: \cup \: B) = \frac{3}{5} + \frac{3 - 4}{10} \\ \\ P(A \: \cup \: B) = \frac{3}{5} - \frac{1}{10} \\ \\ P(A \: \cup \: B) = \frac{2 \times 3 - 1 \times 1}{10} \\ \\ P(A \: \cup \: B) = \frac{6 - 1}{10} \\ \\ P(A \: \cup \: B) = \frac{5 \div 5}{10 \div 5} \\ \\ \Large \boxed{ \green{ \bf \: P(A \: \cup \: B) = \frac{1}{2} }} \\ \\ \Large \boxed{ \underline{ \blue{ \bf \: Bons \: Estudos!}}} \\ \\ \Large \boxed{ \underline{ \bf \: 24/05/2021}}$