Answer:
[tex]Probability = 0.734[/tex]
Step-by-step explanation:
Given
Represent the event that a bulb is defective with p.
So:
[tex]p =6\%[/tex]
Required
Determine the probability that all 5 are fully functioning
Represent the event that a bulb is defective with q.
So:
[tex]p + q = 1[/tex]
Make q the subject
[tex]q = 1 - p[/tex]
Substitute 6% for p
[tex]q = 1 - 6\%[/tex]
Convert % to decimal
[tex]q = 1 - 0.06[/tex]
[tex]q = 0.94[/tex]
If 5 were selected and all are functioning, the event is represented as: q q q q q
And the probability is:
[tex]Probability = q * q * q * q *q[/tex]
[tex]Probability = q^5[/tex]
Substitute 0.94 for q
[tex]Probability = 0.94^5[/tex]
[tex]Probability = 0.7339040224[/tex]
[tex]Probability = 0.734[/tex] --- approximated
