Show in detail that the events length of gestation less than

Show (in detail) that the events {length of gestation less than or equal to 31 weeks} and {low birth weight} are not independent.

Table 3.7 DISTRIBUTION OF LENGTH OF GESTATION

If A and B are dependent events, then the probability of A happening AND the probability of B happening, given A, is P(A) × P(B after A).

P(A and B) = P(A) × P(B after A)

Here,

A = length of gestation less than 31 weeks

P(A) = 0.007 + 0.012 = 0.019 (cumulative probability)

B = chances of a low birthweight

The values of B are given as cumulative values

SO, P(B) = 0.702 when period of gesticulation is below 31 weeks.

P (A and B) = 0.019 * 0.702

= 0.013338

Thus, the events are not independent as that is the only way to find the probability.