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) ?

Question

Mathematics

Emmy Henson

27 May, 13:28

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) ?

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Answers (1)

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Maddison Walsh · Answer 1

Answer:P (Salsa ∩ Pop), The citizens who would like to learn salsa and pop is 30%

Step-by-step 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%