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Lemur [1.5K]
3 years ago
9

A bin contains 64 light bulbs of which 10 are defective. if 5 light bulbs are randomly selected from the bin with replacement, f

ind the probability that all the bulbs selected are good ones. round to the nearest thousandth if necessary.
Mathematics
1 answer:
Sloan [31]3 years ago
3 0
Total number of bulbs = 64
Number of defective bulbs = 10
Number of good bulbs = 64 - 10 = 54

P(5 good bulbs) = (54/64)⁵ = (27/32)⁵ = 0.428


Answer: 0.428
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Step-by-step explanation:

Hi there!

<u>Background of the Discriminant</u>

The discriminant b^2-4ac applies to quadratic equations when they are organised in standard form: ax^2+bx+c=0.

All quadratic equations can be solved with the quadratic formula: x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}.

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When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

<u>Solving the Problem</u>

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We're given the above equation. It hasn't been organised completely in ax^2+bx+c=0, but we can change that by adding 1 to both sides to make the right side equal to 0:

3x^2+5x+1=0<u />

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

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I hope this helps!

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