Question

The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power. The probabilities that these two sources will be successfully developed and commercially viable in the next 10 years are 0.70 and 0.85, respectively. The successful development of these two energy sources are statistically independent. Determine the following: a. The probability that there will be energy supplied by these two alternative sources in the next 10 years. b. The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years.

Answer 1

Answer:

Step-by-step explanation:

a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S

Write the probability of energy supplied by these energy sources in the next 10 years  

P(energy supplied) = P(S ∪ F) -----(1)

Rewrite eqn (1)

P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)

substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources

P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)

= 0.85 + 0.7 - (0.595)

= 1.55 - 0.595

= 0.955

Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955

B) write the probability of only one source of energy available

P(only one source of energy available) = $P(\bar F S)$ ∪ $P( \bar S F)$ ---(3)

Rewrite the equation (3)

P(only one source of energy available) =

$=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)$

$=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36$

Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36