A research project proceeds through four sequential phases , ,

MATHEMATICS · Single correct · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

A research project proceeds through four sequential phases

P_1

P_2

P_3

, and

P_4

with the following probabilities:

P(P_1)=0.9

P(P_2\mid P_1)=0.8

P(P_3\mid P_1 \cap P_2)=x

, and

P(P_4\mid P_1 \cap P_2 \cap P_3)=0.7

. If

P(P_1 \cap P_2 \cap P_3 \cap P_4)=0.2016

, find the value of

x

. (a)

0.32

(b)

0.60

(c)

0.40

(d)

0.28