In a four-stage process

MATHEMATICS · Subjective · CBSE · Mathematics · Probability · Probability

Problem

In a four-stage process, a component must pass tests

T_1, T_2, T_3

and

T_4

in that order. •

P(T_1)=0.85

. • If

T_1

is passed, the probability of passing

T_2

0.80

. •

T_3

is independent of

T_1

and

T_2

, with

P(T_3)=0.90

. • If the first three tests are all passed, the probability of passing

T_4

0.95

. Calculate the probability that a component passes all four tests.