Question

A hiker attempting to cross a wilderness area has two GPS systems of intermittent reliability because of the areas remoteness .from past experience he estimates that at any moment the probability that system I will work is 0.85, that system II will work is 0.90 , and both will work is 0.80 . the probability that at any moment at least one of the systems will work is about___________.A. 0.87
B. 0.92
C. 0.75
D. 0.95
E. 0.88

Answer 1

Answer:

D. 0.95

Step-by-step explanation:

The probability that at any moment, at least one of the systems will work is determined by the probability that system I works, added to the probability that system II works, and subtracted by the probability that both systems work:

$P(S_I\cup S_{II}) =P(S_I)+P(S_{II})-P(S_I\cap S_{II})\\P(S_I\cup S_{II}) =0.85+0.90-0.80\\P(S_I\cup S_{II}) =0.95$

The probability that at any moment at least one of the systems will work is about 0.95.