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

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?

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3 weeks 2021-09-25T12:24:06+00:00 1 Answer 0

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    2021-09-25T12:25:31+00:00

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

    b) 0.193

    c) 0.60

    Step-by-step 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\times 0.051=0.0072

    and

    P(A\cap B)=0.051

    So, we can see that

    P(A).P(B)\neq 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)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.031}{0.051}=0.60

    Hence, a) No,

    b) 0.193

    c) 0.60

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