Answer:
In the case of the production Line, we know that,
No of gasoline cans = 5
probability that 1st can is out of tolerance = 0.03
probability that 2nd can is out of tolerance = 0.03
.
.
probability that the 5th can is out of tolerance = 0.03
Therefore,
probability of 1st can out of tolerance + probability of 1st can not out of tolerance = 1
Probability of 1st can not out of tolerance = 1 -- 0.03 = 0.97
probability of 2nd can not out of tolerance = 0.97
.
.
probability of 5th can not out of tolerance = 0.97
Question A:
Probability that they are all out of tolerance
= P(1st can out of tolerance) * P(2nd can out of tolerance) * P(3rd can out of tolerance) * P(4th can out of tolerance) * P(5th can out of tolerance)
= (0.03 ) * (0.03) * (0.03) * (0.03) * (0.03) = 2.43 E⁻⁸ (2.43 ˣ 10⁻⁸)
Question B:
Probability that exactly two are out of tolerance
= P(1st can is out of tolerance) * P(2nd can is out of tolerance) * P(3rd can is not out of tolerance) * P(4th can is not out of tolerance) * P(5th can is not out of tolerance)
= (0.03) * (0.03) * (0.97) * (0.97) * (0.97) = 0.0008214057
Explanation:
