If the probability of machine failing during a day is 0·95 the probability of its working for four consecutive days without failing is-

Options

A. 6.25E-6
B. 0.0625
C. 0.16548375
D. 0.000625

Answer

To solve the problem, we need to determine the probability of a machine working for four consecutive days without failing, given that the probability of it failing during a day is 0.95.

### Step-by-Step Solution:

**Step 1: Determine the probability of the machine working for one day.**
- The probability of the machine failing in a day is given as \( P(\text{Fail}) = 0.95 \).
- Therefore, the probability of the machine working for one day is:
\[ P(\text{Working}) = 1 - P(\text{Fail}) = 1 - 0.95 = 0.05 \]

**Step 2: Calculate the probability of the machine working for four consecutive days.**
- Since the events are independent (the machine's performance on one day does not affect its performance on another day), we can multiply the probabilities of it working each day.
- Thus, the probability of the machine working for four consecutive days is:
\[ P(\text{Working for 4 days}) = P(\text{Working})^4 = (0.05)^4 \]

**Step 3: Compute \( (0.05)^4 \).**
- Now we calculate \( (0.05)^4 \):
\[ (0.05)^4 = 0.05 \times 0.05 \times 0.05 \times 0.05 = 0.00000625 \]

### Final Answer:
The probability of the machine working for four consecutive days without failing is \( 0.00000625 \).

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