Question

A two-way frequency table shows baldness in men over 45 and men under 45.

Under 45 Over 45 Total
Bald 24 16 40
Not Bald 36 24 60
60 40 100


Based on this data, are baldness and being over 45 independent events?

A) Yes, P(bald | over 45) = P(bald)

B) Yes, P(bald | over 45) = P(over 45)

C) No, P(bald | over 45) _ P(bald)

D) No, P(bald | over 45) _ P(over 45)

Answer 1

If $Pr(A\cap B)=Pr(A)\cdot Pr(B)$, then events A and B are independent, otherwise they are dependent.

Using conditional probabilities this property can be written as:

$Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)}=\dfrac{Pr(A)\cdot Pr(B)}{Pr(B)}=Pr(A)$.

Count the probabilities:

1. $Pr(\text{man is bald})=\dfrac{40}{100} =0.4$

2. $Pr(\text{bald }|\text{ over 45})=\dfrac{16}{40} =0.4$

Then $Pr(\text{bald }|\text{ over 45})=Pr(\text{man is bald})=0.4$ and events are independent.

Answer: correct choice is A.

Answer 2

Answer:

Thy answer is "A) Yes, P(bald | over 45) = P(bald)"

Step-by-step explanation:

I knowith thus because me got thowest question right.

Hope thus has helped~

All thowist love, Ya boi Fraser.