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3 years ago

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Mrs. Jones buys two toys for her son. The probability that the first toy is defective is 1/3, and the probability that the secon

d toy is defective given that the first toy is defective is 1/5. What is the probability that both toys are defective?

2 answers:

Debora [2.8K]3 years ago

6 0

Answer: $\frac{1}{15}$

Step-by-step explanation:

Let F denote the event of first toy is defective and S denote the second toy is defective .

Given: The probability that the first toy is defective $P(F)=\frac{1}{3}$

The probability that the second toy is defective given that the first toy is defective $P(S|F)=\frac{1}{5}$

The formula to calculate the conditional probability is given by :-

$P(S|F)=\frac{P(S\cap F)}{P(F)}\\\\\Rightarrow P(S\cap F)=P(S|F)\times P(F)\\\\\Rightarrow\ P(S\cap F)=\frac{1}{3}\times \frac{1}{5}=\frac{1}{15}$

Hence, the probability that both toys are defective= $\frac{1}{15}$

sergeinik [125]3 years ago

3 0

Answer:

Probability= $\frac{1}{15}$

Step-by-step explanation:

As it is given that

Probability of toy A is defective is =P(A) = $\frac{1}{3}$

Probability of toy b is defective if A is defective = P (B)= $\frac{1}{5}$

WE have to find the P(A n B)

By the law of Probability

P(A n B) = P (A).P(B)

putting the values given to us

P(AnB)= $\frac{1}{3}$ * $\frac{1}{5}$

Probability= $\frac{1}{15}$

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WATER TOWER One of the largest sphere water towers in the country is located in Edmond, Oklahoma. It is 218 feet tall and holds

Fudgin [204]

Answer: The radius of the new water tower is approximately 21 ft^3

Step-by-step explanation:

So we know the volume of the Water Tower is 66840 ft^3 and the new one's volume will hold 3/5 as much. so you will multiply 66840 by 3/5 to find the volume of the new one.

66840 * 3/5 = 40104 so the new water tower will hold 40104 cubic feet of water.

Now to find the radius we will use the formula v= 4/3 $\pi$ r^3

40104 = 4/3 * $\pi$ * r^3

40104= 4.1887* r^3

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3 years ago

The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes

devlian [24]

Answer:

(a) There is no evidence to support the claim that the two machines produce rods with different mean diameters.

P-value is 0.818

(b) 95% confidence interval for the difference in mean rod diameter is (-0.17, 0.27).

This interval shows that the difference in mean is between -0.17 and 0.27.

Step-by-step explanation:

(a) Null hypothesis: The two machines produce rods with the same mean diameter.

Alternate hypothesis: The two machines produce rods with different mean diameter.

Machine 1

mean = 8.73

variance = 0.35

n1 = 15

Machine 2

mean = 8.68

variance = 0.4

n2 = 17

pooled variance = [(15-1)0.35 + (17-1)0.4] ÷ (15+17-2) = 11.3 ÷ 30 = 0.38

Test statistic (t) = (8.73 - 8.68) ÷ sqrt[0.38(1/15 + 1/17)] = 0.05 ÷ 0.218 = 0.23

degree of freedom = n1+n2-2 = 15+17-2 = 30

Significance level = 0.05 = 5%

Critical values corresponding to 30 degrees of freedom and 5% significance level are -2.042 and 2.042.

Conclusion:

Fail to reject the null hypothesis because the test statistic 0.23 falls within the region bounded by the critical values -2.042 and 2.042.

There is no evidence to support the claim that the two machines produce rods with different mean diameters.

Cumulative area of test statistic is 0.5910

The test is a two-tailed test.

P-value = 2(1 - 0.5910) = 2×0.409 = 0.818

(b) Difference in mean = 8.73 - 8.68 = 0.05

pooled sd = sqrt(pooled variance) = sqrt(0.38) = 0.62

Critical value (t) = 2.042

E = t×pooled sd/√n1+n2 = 2.042×0.62/√15+17 = 0.22

Lower limit of difference in mean = 0.05 - 0.22 = -0.17

Upper limit of difference in mean = 0.05 + 0.22 = 0.27

95% confidence interval for the difference in mean rod diameter is between a lower limit of -0.17 and an upper limit of 0.27.

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3 years ago

(0, -2) is a solution of the equation 2x - 3y = 6. true or false

lisov135 [29]

Answer:

It is a solution of the ordered pair.

Step-by-step explanation:

The y intercept is (0,-2)

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3 years ago

What is the length of the altitude of the equilateral triangle below?

Mazyrski [523]

ANSWER

The length of the altitude is $3\sqrt{3}$ units

<u>EXPLANATION</u>

The altitude of a triangle is the vertical height of the triangle.

From the diagram the altitude is $a$

Method 1: We can use Pythagoras theorem to find $a$

$6^2=a^2+3^2$

$6^2-3^2=a^2$

$36-9=a^2$

$27=a^2$

We take the square root of both sides,

$\sqrt{27}=a$

$\sqrt{9\times3}=a$

$\sqrt{9} \times \sqrt{3}=a$

$3\sqrt{3}=a$

Method 2 Using Trigonometry

$sin(60\degree)=\frac{a}{6}$

$6sin(60\degree)=a$

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$a=3\sqrt{3}$

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3 years ago

Read 2 more answers

The value of P where P= (1)2 + (3)2 + (5)2 +......... + (25)?

kramer

Answer:

338

Step-by-step explanation:

1×2=2 2+6+10+14+18+22+26+30

3×2=6 +34+36+38+42+46+50=338

5×2=10

7×2=14

9×2=18

11×2=22

13×2=26

15×2=30

17×2=34

19×2=38

21×2=42

23×2=46

25×2=50

6 0

2 years ago