Question

By accident, six burned-out bulbs have been mixed in with 26 good ones. Ken is replacing old bulbs in his house. If he selects two bulbs at random from the box of 32, what is the probability they both work? (4 points)

Help please

Answer 1

Answer: 325/496

This is the exact probability.

The approximate probability is roughly 0.6552

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Work Shown:

26 working bulbs

6 broken bulbs

26+6 = 32 bulbs total

A = probability Ken picks a working bulb

A = (number of working bulbs)/(number total)

A = 26/32

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B = probability Ken picks another working bulb

B = (number of working bulbs left)/(number total left)

B = (26-1)/(32-1)

B = 25/31

Note how I subtracted 1 from each value after the first working bulb was chosen; this is done since Ken doesn't put the first bulb back.

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C = probability Ken picks two working bulbs in a row

C = A*B

C = (26/32)*(25/31)

C = (26*25)/(32*31)

C = (2*13*25)/(2*16*31)

C = (13*25)/(16*31)

C = 325/496

The probability Ken picks two working bulbs in a row is exactly 325/496

Using a calculator, this is approximately 325/496 = 0.6552

So there's roughly a 65.52% chance of him picking two good bulbs.