Examples on probability, Mathematics

Assignment Help:

1. A machine comprises of three transformers A, B and C. Such machine may operate if at least 2 transformers are working. The probability of each transformer working is given as displayed below;

            P (A) = 0.6,      P (B) = 0.5,      P (C) = 0.7

A mechanical engineer went to inspect the working situations of those transformers. Determine the probabilities of having the given outcomes

i. Only one transformer operating

ii. Two transformers are operating

iii. All three transformers are operating

iv. None is operating

v.  At least two are operating

vi. At most two are operating

Solution

P(A) =0.6                     P(A) = 0.4                    P(B) = 0.5                    P(~B) = 0.5

P(C) = 0.7                    P(C¯) = 0.3

 i.  P(only one transformer is operating) is described by the given possibilities

                         1st                   2nd                  3rd

            P          (A                     B¯                      C¯ )        =  0.6 x 0.5 x 0.3 = 0.09

            P          (A                     B                      C¯ )         = 0.4 x 0.5 x 0.3 = 0.06

            P          (A                     B¯                      C)         = 0.4 x 0.5 x 0.7 = 0.14

∴ P(Only one transformer working)

            = 0.09 + 0.06 + 0.14 = 0.29

ii.  P(only two transformers are operating) is described by the given possibilities. 

                        1st                   2nd                  3rd

            P          (A                     B                      C¯ )        =  0.6 x 0.5 x 0.3 = 0.09

            P          (A                     B¯                     C)          = 0.6 x 0.5 x 0.7 = 0.21

            P          (A                     B                      C)         = 0.4 x 0.5 x 0.7 = 0.14

∴ P(Only two transformers are operating)

 = 0.09 + 0.21 + 0.14 = 0.44

iii.  P(all the three transformers are operating). 

 = P(A) x P(B) x P(C)

 = 0.6 x 0.5 x 0.7

= 0.21

iv.  P(none of the transformers is operating). 

= P(A) x P(B¯) x P(C¯)

= 0.4 x 0.5 x 0.3

= 0.06

v.  P(at least 2 working). 

 = P(exactly 2 working) + P(all three working)

  =  0.44 + 0.21

= 0.65

vi.  P(at most 2 working). 

     =  P(Zero working) + P(one working) + P(two working)

     = 0.06 +  0.29 + 0.44

= 0.79


Related Discussions:- Examples on probability

What does required to earn on his further science test in 93, Justin earned...

Justin earned scores of 85, 92, and 95 on his science tests. What does he required to earn on his further science test to have an average (arithmetic mean) of 93%? To earn an a

Brad class collected 320 cans of food how many did required, Brad's class c...

Brad's class collected 320 cans of food. They boxed them in boxes of 40 cans each. How many boxes did they required? To find the number of boxes required, you should divide the

Decision-making under conditions of certainty, Decision-Making Under Condit...

Decision-Making Under Conditions of Certainty Conditions of certainty tend to be rare, especially when significant decisions are involved. Under conditions of certainty, decis

How many pages can it print in 4 minutes, Tammi's latest printer can print ...

Tammi's latest printer can print 13.5 pages a minute. How many pages can it print in 4 minutes? Multiply 13.5 by 4 to ?nd out the number of copies made; 13.5 × 4 = 54 copies.

Differentiate functions h (t ) = 2t5 + t2- 5 / t2 , Differentiate f...

Differentiate following functions.                       h (t ) = 2t 5 + t 2 - 5 / t 2 We can simplify this rational expression as follows.                       h (t )

Derivatives, Derivatives The rate of change in the value of a...

Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is

How many can speak both english and russian, In a group of 1000 people, the...

In a group of 1000 people, there are 750 people will speak English and 400 people will speak Russian. How many may speak English only? How many will speak Russian? How many can spe

Fundamental theorem of calculus, Fundamental Theorem of Calculus, Part I ...

Fundamental Theorem of Calculus, Part I As noted through the title above it is only the first part to the Fundamental Theorem of Calculus. The first part of this theorem us

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd