Answered

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A light bulb manufacturing process results in 6% of the light
bulbs being defective. If 5 light bulbs are randomly
selected, find the probability that all of the light bulbs are
fully functioning.

Sagot :

MrRoyal

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

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