Question 3 (2 points)

A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

zavuch27 [327]

SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes

$\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}$

hence the answer is 0.4823

(iii) All are defective

$\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}$

(iv) At least one is defective

This is 1 - probability that none is defective

$\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}$

Hence the answer is 0.5177

3 0

1 year ago

Last year, a professional basketball team

jarptica [38.1K]

Answer:

15%

Step-by-step explanation:

Take 9 and divide that by 60.

8 0

2 years ago

PLEASE HELP! I am having trouble with both questions

schepotkina [342]

Answer:

someone had the same exact question i just helped him on it sub 4 for x and 1 for h

Step-by-step explanation:

6 0

2 years ago

Which of the following could be the perimeter of a rectangle with an area of 16 square inches?

emmasim [6.3K]

Answer:

16 inches

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A neighbor farmer had some chickens. She had 24 feet of wire fencing to

Paraphin [41]

Answer:

A rectangle is defined by its length = L, and its width = W.

So the perimeter of the of the rectangle can be written as:

Perimeter = 2*L + 2*W.

In this case, we want to leave the perimeter fixed, so we have:

24ft = 2*L + 2*W.

Now, we do not have any other restrictions, so to know the different dimensions now we can write this as a function, by isolating one of the variables.

2*L = 24ft - 2*W

L = 12ft - W.

or:

L(W) = 12ft - W.

Such that:

W must be greater than zero (because we can not have negative or zero width).

And W must be smaller than 12ft (because in that case we would have zero or negative length)

Then the possible different dimensions are given by:

L(W) = 12ft - W

0ft < W < 12ft.

8 0

3 years ago