Question

In a small town, the new community center will be offering salsa and pop dance classes. After a survey of the community, they found that 90% of the citizens would like to learn salsa or pop dance, would like to learn 50% salsa, and 70% would like to learn pop dance. What is P(Salsa ∩ Pop)?

Answer 1

P(Salsa ∩ Pop), The citizens who would like to learn salsa and pop is

30%

Explanation:

Let A be the event of citizens to learn salsa

Le B be the event of citizens to learn pop

The citizens who would like to learn salsa, P (A) = 50 %

The citizens who would like to learn pop, P (B) = 70 %

The citizens who would like to learn salsa or pop, P (A U B) = 90 %

The citizens who would like to learn salsa and pop, P (A ∩ B) = ??

By formula,

P (A U B) = P (A) + P (B) - P (A ∩ B )

Sbstituting the values in the above equation, we get

90 = 50 + 70 - P (A ∩ B )

P (A ∩ B ) = 120 - 90

P (A ∩ B ) = 30%