Question

A class have 100 students
A : student study history is 0.4
B: student study math 0.5

a) calculate probability is that at least 1 student studied one of two subjects
b) calculate probability is that none of the students studied one of the two subjects
c) calculate probability is that 1 student study history, don't study math

Answer 1

Answer on Question #70922 – Math – Statistics and Probability Question

A class have 100 students

A: student study history is 0.4

B: student study math 0.5

a) calculate probability is that at least 1 student studied one of two subjects

b) calculate probability is that none of the students studied one of the two subjects

c) calculate probability is that 1 student study history, don't study math

Solution

Let $A \cap B =$ 'student study both math and history'.

a) The probability that at least 1 student studied one of two subjects is

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ $$P(A \cup B) = 0.4 + 0.5 - P(A \cap B) = 0.9 - P(A \cap B)$$

b) The probability that none of the students studied one of the two subjects is

$$P((A \cup B)^c) = 1 - P(A \cup B) = 1 - (0.9 - P(A \cap B)) = 0.1 + P(A \cap B)$$

c) The probability is that 1 student study history, don't study math

$$P(\text{History not Math}) = P(A) - P(A \cap B) = 0.4 - P(A \cap B)$$

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