Question

Smoking by Race for Males Aged 18-24

Smoker Nonsmoker Row Total
(S) (N)
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
Calculate the probabilities given below (Round your answers to 4 decimal places.):
i. P(S) 0.3200
ii. P(W) 0.8500
iii. P(S | W) 0.2720
iv. P(S | B) 0.0300
v. P(S and W) 0.9062
vi. P(N and B) 0.1765

Answer 1

(i) 0.32 (ii) 0.85

(iii) 0.3412 (iv) 0.20

(v) 0.29 (vi) 0.12

Explanation:

The data provided is as follows:

Race Smoker (S) Nonsmoker (N) Row Total

White(W) 290 560 850

Black(B) 30 120 150

Column Total 320 680 1,000

(i)

Compute the value of P (S) as follows:

`P(S)=(n(S))/(N)=(320)/(1000)=0.32`

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

`P(W)=(n(W))/(T)=(850)/(1000)=0.85`

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

`P(S|W)=(n(S\cap W))/(n(W))=(290)/(850)=0.3412`

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

`P(S|B)=(n(S\cap B))/(n(B))=(30)/(150)=0.20`

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

`P(S\cap W)=(n(S\cap W))/(T)=(290)/(1000)=0.29`

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

`P(N\cap B)=(n(N\cap B))/(T)=(120)/(1000)=0.12`

P (S∩W) = 0.12.