Question

For Mexican American infants born in Arizona in 1986 and 1987, the probability that a child's gestational age is less than 37 weeks is 0.142 and the probability that his or her birth weight is less than 2500 grams is 0.051. Furthermore, the probability that these two events occur simultaneously is 0.031. Please show work!a. are A and B independent?b. For a randomly selected Mexican American newborn, what is the probability that A or B or both occur?c.What is the probability that event A occurs given that event B occurs?

Answer 1

Answer: Hence, a) No, they are not independent

b) 0.193

c) 0.60

Explanation:

Since we have given that

Probability that a child's gestational age is less than 37 weeks say P(A)= 0.142

Probability that his or her birth weight is less than 2500 grams say P(B) = 0.051

P(A∩B) = 0.031

We need to check whether it is independent or not.

Since ,

`P(A).P(B)=0.142* 0.051=0.0072`

and

`P(A\cap B)=0.051`

So, we can see that

`P(A).P(B)\\eq P(A\cap B)`

So, it is not independent.

a) Hence, A and B are not independent.

b) P(A∪B) is given by

`P(A\ or B\ or\ both)=P(A)+P(B)\\\\P(A\ or\ B\ or\ both)=0.142+0.051=0.193`

c) P(A|B) is given by

`P(A\mid B)=(P(A\cap B))/(P(B))=(0.031)/(0.051)=0.60`

Hence, a) No,

b) 0.193

c) 0.60