Ask question

Ask question

All categories

3 years ago

15

The probability that a certain kind of component will survive a shock test is 3/4. Find the probability that exactly 2 of the ne

xt 4 components tested survive test, assuming tests are independent.

1 answer:

Marina86 [1]3 years ago

3 0

Answer:

Therefore the required probability is $=\frac{27}{128}$

Step-by-step explanation:

The probability of success is $\frac{3}{4}$

The number of trial = 4

X= the items survive out of 4

$P(x=r)=^nC_rq^{n-r}p^r$ p =the probability of success and q = the probability failure.

p= $\frac{3}{4}$ and $q=(1-\frac{3}{4})=\frac{1}{4}$

$\therefore P(X=2)=^4C_2(\frac{1}{4} )^2(\frac{3}{4} )^2$

$=\frac{4!}{2!2!} (\frac{1}{16} )(\frac{9}{16} )$

$=\frac{27}{128}$

Therefore the required probability is $=\frac{27}{128}$

You might be interested in

Apply Newton’s method to estimate the solution of x3 − x − 1 = 0 by taking x1 = 1 and finding the least n such that xn and xn +

ss7ja [257]

Solution :

Given

$f(x)=x^3-x-1, x_1=1$

$f'(x)=3x^2-1$

Let the initial approximation is $x_1 =1$

So by Newton's method, we get

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)},n=1,2,...$

$x_2=x_1-\frac{f(x_1)}{f'(x_1)}=1-\frac{1^3-1-1}{3(1)^2-1}=1.5$

$x_3=1.5-\frac{(1.5)^3-1.5-1}{3(1.5)^2-1}=1.34782608$

$x_4=1.34782608-\frac{(1.34782608)^3-1.34782608-1}{3(1.34782608)^2-1}=1.32520039$

$x_5=1.32520039-\frac{(1.32520039)^3-1.32520039-1}{3(1.32520039)^2-1}=1.32471817$

$x_6=1.32471817-\frac{(1.32471817)^3-1.32471817-1}{3(1.32471817)^2-1}=1.32471795$

$x_5 \approx x_6$ are identical up to eight decimal places.

The approximate real root is x ≈ 1.32471795

∴ x = 1.32471795

4 0

3 years ago

In circle A shown below, the measure of ∠BAD is 148°: Circle A with angle BAD measuring 148 degrees; points B, C, D lie on Circl

german

Answer:

52°

Step-by-step explanation:

In the figure attached, Circle A is shown. There we can see that:

∠BC + ∠CD = ∠BAD

We know that Arc BC measures 96° and arc BAD measures 148°. Replacing this data into the equation and solving for Arc CD, we get:

96° + ∠CD = 148°

∠CD = 148° - 96°

∠CD = 52°

5 0

2 years ago

Probability The average time between incoming calls at a switchboard is 3 minutes.if a call has just come in,the probability tha

Stels [109]

Answer:

a) 0.1535

b) 0.4866

c) 0.8111

Step-by-step explanation:

The probability that the next call come within the next t minutes is:

$p(t) = 1 -e ^{- t/3}$

According to this model,

a) the probability that a call in comes within 1/2 minutes is $p(t) = 1 -e ^{- (1/2)/3}$ =0.1535

b) the probability that a call in comes within 2 minutes is $p(t) = 1 -e ^{-2/3}$ =0.4866

c) the probability that a call in comes within 5 minutes is $p(t) = 1 -e ^{-5/3}$ =0.8111

6 0

3 years ago

You have invested in three different stocks: Engineering Aces, Upton Clothiers, and Thompson Musical Instruments. Because you ha

Serga [27]

Answer:

answer is 0.001254.

Step-by-step explanation:

Given that you invested in 3 stocks of Engineering Aces, Upton Clothiers, and Thompson Musical Instruments.

Also given that each stock value is independent of the other.

Let E be the event changing in value by more than 10% in a given week for Engineering Aces,

U be the event changing in value by more than 10% in a given week for Upton Clothiers, and T be the event changing in value by more than 10% in a given week for Thompson Musical Instruments.

Given that P(E) = = 19%

P(U) = 11%

P(T) = 6%

probability that all three will change by more than 10% in the same week

= P(EUT)

= P(E) P(U) P(T) since three events are independent.

=0.19(0.11)0.06

= 0.001254

8 0

3 years ago

Karissa says that to represent the expression - 7 - (- 9) on number line, she should start at 7 and move units to the IN correct

Sholpan [36]

Answer:

No

Step-by-step explanation:

Should start at -7 and move 9 units towards right (in the positive direction).

Should stop at 2

8 0

3 years ago