In a factory there are 100 units of a certain product, 5 of which are defective. We pick three units from the 100 units at random. What is the probability that none of them are defective

The probability that none of the picked products are defective is;

P(None picked is defective) = 0.856

This means the number of good products that are not defective are 95.

95/100 × 94/99 × 93/98 = 0.856

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Probability of picking all three non-defective units

= 7372/8085  (or 0.911812 to six decimals)

Step-by-step explanation:

Let

D = event that the picked unit is defective

N = event that the picked unit is not defective

Pick are without replacement.

We need to calculate P(NNN) using the multiplication rule,

P(NNN)

= 97/100 * 96/99 * 95/98

=7372/8085

= 0.97*0.969697*0.9693878

= 0.911812

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

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