Answer: 0.0052
Step-by-step explanation:
Total number of times experiment was performed (n)= 12
Probability of the event (that one key out of a total of 12 opens the door) = 1/12 = 0.083
Hence, p = 0.83
q = 1 - p = 11/12 = 0.917
x = 3
Since the experiment was performed n number of times, a binomial probability distribution can defined the experiment.
P(x=r) = nCr ×p^r × q^n-r
P(x=3) = 12C3 × (0.083)⁴ × (0.917)^8
P(x=3) = 220 × (0.083)⁴ × (0.917)^8
P(x=3) = 0.0052
