-defectives Frve chips \"re removed at a) En how w ao) what is the probby SKuty

Question

-defectives Frve chips "re removed at a) En how w ao) what is the probby SKuty one of the chosen chips are defective any ways qan this be done? the Cheese Ckes A delivery service offers both express and standard delivery. Eighty percent of parceis are sent by andard delivery, and 20% are sent by express or those sent standard, 75% se sent express, 95% arrive the next day. A record of a parcel delivery pany's tiles arrive the next day, and of is chosen at random from the (a) What is the probability that the parcel was shipped express and arrived the next day Cb) What is the probability that it arrived the next day (e) Given that the package arrived the next day, what is the probability that it was sent express production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as may ine 2. One percent of the bags from Line 1 are defective in that they fail to meet a cation, while 3% of the bags from Line 2 are defective. A bag is randomly chose on. If the bag is not defective, what is the probability that it came from Line 1? 2. 01) t (1-4) ble X' has a density function given by f() value ofk 0 otherwise

Explanation / Answer

A)

let the

S--> be the event that parcel is send by standard delivery

E-->be the event that parcel is send by express

therfore P(E) = 20%=0.2

P(S)=80%=0.8

a)

P ( shipped by expess and arrive on next day )= P( E) * P ( arriving next day when sent by express)

=0.2*0.95=0.19

b)

P ( arriving next day)=P( sending by standard delivery )P( arriving when send by standard delivery)+ P( sending by Express )P( arriving when send by Express)

= 0.8*0.75 + 0.2*0.95

=0.79

c)

let A -> be the event of arriving parcel on next day

from above P(A)=0.79

we have to calculate P(E/A)

using formula

P( E ^ A )=P(E)*P(A/E)=P(A)*P(E/A)

0.2*0.75= 0.79*P(E/A)

P(E/A)=0.2*0.75/0.79=0.1899

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