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Musya8 [376]
3 years ago
10

The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that

either event A or event B occurs is 0.6, what is the probability that event B will occur
Mathematics
1 answer:
ICE Princess25 [194]3 years ago
4 0

Answer:

The probability that event B will occur is 0.45

Step-by-step explanation:

Given;

probability that event A occurs, P(A) = 0.4

the probability that events A and B both occur, P(A ∩ B) = 0.25

the probability that either event A or event B occurs, P(A ∪ B) = 0.6

To determine the probability that event B will occur, we use probability addition rule;

P(A) + P(B) = P(A ∩ B) + P(A ∪ B)

0.4 + P(B) = 0.25 + 0.6

0.4 + P(B) = 0.85

P(B) = 0.85 - 0.4

P(B) = 0.45

Therefore, the probability that event B will occur is 0.45

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3 0
2 years ago
What is the decimal equivalent of 6/13 ? Round to tenths place. If answer doesn't
Arte-miy333 [17]

Answer:

0.5

Step-by-step explanation:

6/13 is the same as saying 6 ÷ 13

6 ÷ 13 = 0.4615384615

The first position after the decimal is the tenths column. Round up, because 6>5.

6 0
2 years ago
If x = 7 and y = 4, then x + 2y =
solong [7]
15!

x + 2y = ?
(7) + 2(4) = ?
7 + 8 = 15
8 0
3 years ago
Based on a sample of 100 employees a 95% confidence interval is calculated for the mean age of all employees at a large firm. Th
babymother [125]

Answer:

a

\= x  =  40.85

b

E = 5.85

Ca  

   t_c =  2.08

Cb

   t_c  =   1.282

Explanation:

From the question we are told that

     The sample size is n  =  100

     The upper limit of the 95% confidence interval is  b =  47.2 years

     The lower limit of the 95% confidence interval is   a =  34.5 years

Generally the sample mean is mathematically represented as

         \= x  =  \frac{a + b }{2}

=>    \= x = \frac{47.2 + 34.5 }{2}

=>    \= x  =  40.85

Generally the margin of error is mathematically represented as

         E =  \frac{b- a }{ 2}

=>      E =  \frac{47.2- 34.5 }{ 2}

=>      E = 5.85

Considering question C a  

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90 ) \%

=>   \alpha = 0.10

The  sample size is  n =  22

Given that the sample size is not sufficient enough i.e n < 30 we will make use of the student t distribution table  

Generally the degree of freedom is mathematically represented as

           df =  n- 1

=>        df =  22 - 1

=>        df =  21

Generally from the student  t  distribution table the critical value  of  \frac{\alpha }{2} at a degree of freedom  of  21 is  

   t_c =t_{\frac{\alpha }{2} ,  21  } =  2.08

Considering question C b

From the question we are told the confidence level is  80% , hence the level of significance is    

      \alpha = (100 - 80 ) \%

=>   \alpha = 0.20

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   t_c  =Z_{\frac{\alpha }{2} } =  1.282

4 0
3 years ago
What is the volume of the cone to the nearest whole number?<br><br><br>HELP PLZ
goldfiish [28.3K]

Answer:

167.467mm^3

Step-by-step explanation:

Volume of cone:1/3hpir^2

1/3(10)(pi)(4)^2

=160/3(pi)

(Pi=3.14)

160/3pi=167.467mm^3

4 0
3 years ago
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