Question

1. Mr. Conners surveys all the students in his Geometry class and identifies these probabilities.

The probability that a student has gone to United Kingdom is 0.28.
The probability that a student has gone to Japan is 0.52.
The probability that a student has gone to both United Kingdom and Japan is 0.14.
What is the probability that a student in Mr. Conners’ class has been to United Kingdom or Japan?

Answer 1

To find the probability that a student in Mr. Conners' class has been to either the United Kingdom or Japan, we need to calculate the union of the probabilities for each country and subtract the probability of both events occurring.

Let's denote:
P(UK) = probability that a student has gone to the United Kingdom = 0.28
P(Japan) = probability that a student has gone to Japan = 0.52
P(UK and Japan) = probability that a student has gone to both the United Kingdom and Japan = 0.14

The probability of the union of two events (A or B) can be calculated using the formula:
P(A or B) = P(A) + P(B) - P(A and B)

Applying this formula to our scenario:
P(UK or Japan) = P(UK) + P(Japan) - P(UK and Japan)
= 0.28 + 0.52 - 0.14
= 0.80

Therefore, the probability that a student in Mr. Conners' class has been to the United Kingdom or Japan is 0.80, or 80%.