Anthony surveys a group of students at his school about whether they play a
sport. This table shows the results broken down by gender.
Play a sport
Total
Do not play a
sport
105
70
175
Boys
Girls
75
50
125
Total
180
120
300
Are being a girl and playing a sport Independent events? Why or why not?
O A. Yes, they are independent, because P(girl) = 0.58 and Pgirl plays
a sport) = 0.6.
O B. Yes, they are independent, because (girl) = 0.42 and girl plays
a sport) - 0.42
O c. No, they are not independent, because P(girl) = 0.42 and
P(girl plays a sport) = 0.42.
D. Yes, they are independent, because (girl) = 0.58 and P(girl plays
a sport) = 0.58

"These are the events whose occurrence is not dependent on any other event."
"When the probability of occurrence of an event A is not affected by the occurrence of another event B, then event A and event B are independent events."

"If A and B are independent events then, P(A∩B) = P(A).P(B)"

"It is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

P(A) = n(A)/n(S)

where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

For given question,

We have been given a table that shows the results broken down by gender.

Play sports Do not play sports Total

Boy 105 75 180

Girl 70 50 120

Total 175 125 300

Using the definition of probability:

⇒ P(girl) = Number of girls/ Number of students

⇒ P(girl) = 120/300

⇒ P(girl) = 0.4 ....................(1)

Now we find the probability of girls that play a sport.

Using the definition of probability:

P(girl plays a sport)

= Number of girls who plays a sport/ number of students who plays a sport

= 70/ 175

= 0.4 ......................(2)

From (1) and (2),

P(girl) = P(girl plays a sport)

Thus, being a girl and playing a sport are Independent events.

Learn more about independent events here

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