SOLUTION: The probability of a successful optical alignment in the assembly of an optical data storage product is 0.629. Assume that the trials are independent. (Please enter your ans

Question 1130975: The probability of a successful optical alignment in the assembly of an optical data storage product is 0.629. Assume that the trials are independent.

(Please enter your answers as fractions in lowest terms or as decimals rounded to four decimal places. Thank you!)

a. What is the probability that the first successful alignment requires exactly 7 trials?

b. What is the probability that the first successful alignment requires at most 4 trials?

c. What is the probability that the first successful alignment requires at least 6 trials?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The first 6 are unsuccessful is 0.371^6
the 7th is successful with probability 0.629
Their product is 0.0016
at most 4 trials means fewer than 5 trials.
4 trials would be 0.371^3*0.629=0.0321
3 trials would be 0.371^2*0.629=0.0866
2 trials would be 0.371*0.629=0.2334
1 trial would be 0.629
This sum is 0.9811
at least 6 trials would be 0.371^5*0.629=0.0044 for 6
for 7 it is 0.0016 from above
for 8 it is 0.371^7*0.629=0.0006
for 9 it is 0.0002
for 10 it is 0.0001
The sum is 0.0069
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