Question

In a test of a printed circuit board using a random test pattern, an array of 10 bits is equally likely to be 0 or 1. assume the bits are independent. what is the probability that:

(a) all bits are 1s?

Answer 1

The probability that all 10 bits on a printed circuit board are 1s is 0.0009765625, or approximately 0.0977%, calculated using the product of individual bit probabilities since the bits are independent.

Step-by-step explanation:

To solve the mathematical problem completely, we will calculate the probability that all 10 bits on a printed circuit board are 1s, given that each bit is equally likely to be 0 or 1, and that the bits are independent.

The probability of getting a 1 on a single bit is 0.5 since the bit can either be 0 or 1. Because the bits are independent, the probability of all 10 bits being 1s is the product of the probabilities for each bit:

• Probability(all bits are 1s) = (Probability of 1 bit being 1) ¹⁰
• Probability(all bits are 1s) = (0.5) ¹⁰
• Probability(all bits are 1s) = 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5
• Probability(all bits are 1s) = 0.000 0 97 65

Therefore, the probability that all 10 bits are 1s is 0.0009765625, or approximately 0.0977%.