Question

A group of athletic people were asked whether they played soccer or basketball.

Answer 1

Answer:

C. Playing soccer and basketball are not independent since P(soccer|basketball) ≠ P(soccer) and P(basketball|soccer) ≠ P(basketball) .

Step-by-step explanation:

We are given the data of athletic people that played soccer and basketball.

Let,

P(A) = probability of people who played soccer

P(B) = probability of people who played basketball

P(A∩B) = probability of people who played both soccer and basketball.

Now, we find the probability of soccer | basketball

i.e. $P(A|B)=\frac{P(A \bigcap B)}{P(B)}$

i.e. $P(A|B)=\frac{0.3}{0.7}$ = i.e. $P(A|B)=0.43$

As, $P(A|B)=0.43$ ≠ $P(B)=0.7$

So, options A, B and D are discarded.

Moreover, i.e. $P(B|A)=\frac{P(B \bigcap A)}{P(A)}$

i.e. $P(B|A)=\frac{0.3}{0.5}$ = i.e. $P(B|A)=0.375$

i.e. $P(B|A)=0.375$ ≠ $P(A)=0.5$

Hence, playing soccer and basketball are not independent.

Answer 2

Answer:

Your answer would be C.

hope this helps!