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ikadub [295]
3 years ago
12

Consider testing batteries coming off an assembly line one by one until one having a voltage within prescribed limits is found.

The simple events are E1= {S}, E2= {FS}, E3= {FFS} and so on .Suppose the probability of any particular battery being satisfactory is 0.99. All Ei are disjoints. Write down complete sample space and prove that P (sample space) =1.
Mathematics
1 answer:
sleet_krkn [62]3 years ago
5 0
It's clear enough that

\mathbb P(E_i)=\mathbb P(i=j)=\begin{cases}0.99&\text{for }j=1\\0.01\times0.99&\text{for }j=2\\0.01^2\times0.99&\text{for }j=3\\\vdots\end{cases}

Because each of the E_i are disjoint, it follows that

\displaystyle\mathbb P(\text{sample space})=\mathbb P(E_1\cup E_2\cup\cdots)=\mathbb P\left(\bigcup_{i=1}^\infty E_i\right)=\sum_{i=1}^\infty\mathbb P(E_i)
=0.99+0.01\times0.99+0.01^2\times0.99+\cdots
=0.99(1+0.01+0.01^2+\cdots)
=0.99\displaystyle\sum_{n=0}^\infty 0.01^n
=0.99\times\dfrac1{1-0.01}
=\dfrac{0.99}{0.99}=1
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2 years ago
Suppose a die is tossed 5 times. what is the probability of getting exactly 2 fours?
Tasya [4]

Answer:

the probability of getting exactly 2 fours is 0.16

Step-by-step explanation:

The probability of obtaining a number that is four = ¹/₆

The probability of obtaining a non 4 number = 1 - ¹/₆ = ⁵/₆

The number of ways 2 fours can be arrange in five numbers = ⁵C₂ = 10 ways

If the die is tossed five times, the probability of the events is calculated as;

P = 10 x (¹/₆)² x (⁵/₆)³

P = 10 x (¹/₃₆) x  (¹²⁵/₂₁₆)

P = 10 x 0.02778 x 0.5787

P = 0.16

Therefore, the probability of getting exactly 2 fours is 0.16

7 0
2 years ago
Simplify 3ab + 4ab + 5<br><br> 12ab<br> 7ab + 5<br> not possible
Tanya [424]
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3 0
3 years ago
Read 2 more answers
pam deposited $6,900 in a savings account with simple interest. Four months later she had earned $23 in interest. What was the i
3241004551 [841]

Answer:

1%

Step-by-step explanation:

We use the simple interest equation of A=P(1+rt).

A-the total amount with interest earned

P-the initial amount or principal

r-rate

t-time in years

We substitute the values P=6900, A=6923, and t=0.33 since 4 months divided by 12 months is 0.333 years. We then solve for r.

6923=6900(1+r(0.33))\\6923=6900(1+0.33r)\\\frac{6923}{6900} =\frac{6900(1+0.33r)}{6900} \\1.0033=1+0.33r\\1.0033-1=1-1+0.33r\\0.0033=0.33r

Our final step is to divide both sides by 0.33.

\frac{0.0033}{0.33} =\frac{0.33r}{0.33} \\0.01=r

This is the decimal of the rate. We convert to a percentage by multiplying by 100. 0.01(100)=1%.


5 0
2 years ago
I need help with #7 c and d
Misha Larkins [42]

Answer:

  c. 33.0%

  d. 14.5%

Step-by-step explanation:

For answering questions about percentages in different categories or combinations of categories, it is convenient to find the totals of rows and columns in the table. These totals are shown in the attached.

__

<h3>c.</h3>

Students who surf total 32+65 = 97. Of those, 32 also skateboard. The requested percentage is ...

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<h3>d.</h3>

The total number of students is 166. Of those, the number who neither surf nor skateboard is 24. That percentage is ...

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<em>Additional comment</em>

a. 97/166 ≈ 58.4% surf

b. 89/166 ≈ 53.6% do not skateboard

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This sort of table is called a "two-way table." One set of categories is represented in rows, another set is represented in columns. This table is filled with <em>frequencies</em>. Such tables can also display <em>relative frequencies</em> by dividing the entire table by the total of totals in the lower right corner.

3 0
1 year ago
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