Answer:
73.03% probability that it will be working two days from now
Step-by-step explanation:
The machine is broken today.
If the machine is broken on a day, the following day, it has a 1-0.33 = 0.67 probability of working on the next day.
Otherwise, if it is works correctly on a day, it has a 0.76 probability of working on the next day.
Uf the machine is broken today, what is the likelihood that it will be working two days from now
Either of these outcomes are acceptable:
Tomorrow - 2 days from now
Not working - working
Working - Working
Not working - working
Today, it does not work. So tomorrow the probability of not working correctly is 0.33. Then, if tomorrow does not work, 0.67 probability of working correctly two days from now
0.33*0.67 = 0.2211
Working - Working
Today, it does not work. So tomorrow the probability of working correctly is 0.67. Then, if tomorrow works, 0.76 probability of working correctly two days from now
0.67*0.76 = 0.5092
Total
0.2211 + 0.5092 = 0.7303
73.03% probability that it will be working two days from now
