Suppose there are 4 defective batteries in a drawer with 10 batteries in it. A sample of 3 is taken at random without replacement. Let X denote the number of defective batteries in the sample. Find the probability that the sample contains a) Exactly one defective battery b) at most one defective battery. c) at least one defective battery.

a.) 0.5

b.) 0.66

c.) 0.83

Step-by-step explanation:

As given,

Total Number of Batteries in the drawer = 10

Total Number of defective Batteries in the drawer = 4

⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6

Now,

As, a sample of 3 is taken at random without replacement.

a.)

Getting exactly one defective battery means -

1 - from defective battery

2 - from non-defective battery

So,

Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ =   ×

                                                                            = ×

                                                                            = ×

                                                                            = ×

                                                                            = × = 60

Total Number of possibility = ¹⁰C₃ =

                                                        =

                                                        =

                                                        =

                                                        = 120

So, probability =

b.)

at most one defective battery :

⇒either the defective battery is 1 or 0

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 0 , then 3 non defective

Possibility   = ⁴C₀ × ⁶C₃

                   =   ×

                   = ×

                   = 1 ×

                   = 1×

                   = 1 × 20 = 20

getting at most 1 defective battery = 60 + 20 = 80

Probability =

c.)

at least one defective battery :

⇒either the defective battery is 1 or 2 or 3

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 2 , then 1 non defective

Possibility   = ⁴C₂ × ⁶C₁

                   =   ×

                   = ×

                   = ×

                   = ×

                   = 6 × 6 = 36

If the defective battery is 3 , then 0 non defective

Possibility   = ⁴C₃ × ⁶C₀

                   =   ×

                   = ×

                   = × 1

                   = 4×1 = 4

getting at most 1 defective battery = 60 + 36 + 4 = 100

Probability =

The answer is in the image 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

tip=18% of 75.45

     =18/100 * 75.45 = $13.581

Tip = $13.581

Given height of gymnasium is 5/6 height of 30 foot ball

therefore height of gymnasium=5/6 * 30

=25 feet

We can put the numbers in ascending order-

36, 38, 39, 39, 40, 47, 48, 51

Range=max-min

          =51-36

          =15

(​1 or 7) ; number of possible outcome = 2

(a, e,​ i, o, or​ u) ; number of possible outcome = 5

So,

Number of possible outcomes = 2 x 5

Number of possible outcome =10