Answer to Question #93487 in Geometry for jenny

Question

In a math​ class, 45​% of the students have visited the ocean and 55​% have visited the mountains on vacation before. If 40​% of the students have visited the ocean and the mountains on vacation​ before, what is the probability that a randomly selected student has visited the ocean or the​ mountains?

Answer 1

Solution:

Let us consider Ocean Visit as event A and Mountain Visit as event B

Probability of Ocean visit P(A) = 0.45;

Probability of Mountain visit P(B) = 0.55.

Probability of Ocean Visit and Mountain Visit P(A $\bigcap$ B ) = 0.40.

Here P (A$\bigcap$ B) means Probability of event A and event B both happen.

P (A $\bigcup$ B) = P(A) + P(B) - P(A $\bigcap$ B)

where P(A $\bigcup$ B) means Probability of event A or event B happen

P(A $\bigcup$ B) = 0.45 + 0.55 - 0.40

P(A $\bigcup$ B) = 1 - 0.40

P(A $\bigcup$ B) = 0.60

Answer : the Probability of students visited oceans or mountains is 0.60