Question

9. Consider the following information about a group of 151 FCC students:GenderRight-handedLeft-handedTotalFemale492069Male631982Total11239151If one person is randomly selected from the group, what is the probability that this student is male or left-handed?

Answer 1

In this problem, we have to compute an "or" probability. The formula to calculate the “or” probability of two events A and B is this:

`P(\text{A or B)}=P(A)+P(B)-P(\text{A and }B)\text{.}`

We define:

• A = the randomly selected person is male,

,

• B = the randomly selected person is left-handed.

The probabilities that we need are:

• P(A) = # male persons / total # of persons = 82/151,

,

• P(B) = # left-handed persons / total # of persons = 39/151,

,

• P(A and B) = # of persons male and left-handed / total # of persons = 19/151.

Replacing the data in the formula above, we get:

`P(\text{A or B)}=(82)/(151)+(39)/(151)-(19)/(151)=(102)/(151).`

Answer

The probability that a student is male or left-handed is 102/151, or approximately 67.55%.