Question

In a group of 100 students, 50 study Maths, 29 study Biology, and 13 study both.

Draw a Venn diagram and use it to find:
M
P(M)=
P (M') =
P(MNB) =
P(MUB) =
B
e
P(B) =
n
P(MOB) =
P(B') =

Answer 1

Explanation:

-----------------------

| M' |

|---------------------|

| | |

| | |

| B | MB |

| | |

| | |

|---------------------|

| M |

-----------------------

Using the diagram, we can find:

M: The number of students who study Maths is 50, so M = 50.

P(M): The probability of selecting a student who studies Maths is P(M) = M / N = 50 / 100 = 0.5.

P(M'): The probability of selecting a student who does not study Maths is P(M') = 1 - P(M) = 1 - 0.5 = 0.5.

P(MNB): The probability of selecting a student who studies both Maths and Biology is P(MNB) = 13 / 100 = 0.13.

P(MUB): The probability of selecting a student who studies either Maths or Biology (or both) is P(MUB) = (M + B - MB) / N = (50 + 29 - 13) / 100 = 0.66.

B: The number of students who study Biology is 29, so B = 29.

P(B): The probability of selecting a student who studies Biology is P(B) = B / N = 29 / 100 = 0.29.

P(MOB): The probability of selecting a student who studies Maths or Biology (but not both) is P(MOB) = (M + B - 2MB) / N = (50 + 29 - 2(13)) / 100 = 0.64.

P(B'): The probability of selecting a student who does not study Biology is P(B') = 1 - P(B) = 1 - 0.29 = 0.71