A calculator requires a keystroke assembly and a logic circuit. Assume that 83% of the keystroke
assemblies and 92% of the logic circuits are satisfactory. Find the probability that a finished
calculator will be satisfactory. Assume independence of keystroke assemblies and logic circuits.
The probability of several events all occurring is found by multiplying the probability of the individual events.
To find the probability that a finished calculator will be satisfactory, we need to calculate the probability that both the keystroke assembly and the logic circuit are satisfactory.
Let's define:
A = event that the keystroke assembly is satisfactory
B = event that the logic circuit is satisfactory
We are given:
P(A) = 83% = 0.83 (probability keystroke assembly is satisfactory)
P(B) = 92% = 0.92 (probability logic circuit is satisfactory)
Since the keystroke assemblies and logic circuits are assumed to be independent, we can calculate the probability that both A and B occur by multiplying their individual probabilities:
P(A ∩ B) = P(A) × P(B)
Substituting the given values:
P(A ∩ B) = 0.83 × 0.92
Calculating this product gives us the probability that both the keystroke assembly and the logic circuit are satisfactory.