If a sample of 6 keyboards is randomly selected, what is the probability that at least 5 of these will have a mechanical defect

0.1978 is the probability that at least 5 keyboards will have mechanical defect.

Step-by-step explanation:

Solution:

Given:

A repair facility has 25 failed keyboards.

10 keyboards have electrical defect.

15 of which have mechanical defect.

Randomly selected keyboard= 6

The set of A is the set of keyboards with electrical defect.

And  the set of B is set of keyboards with mechanical defect.

N(A U B) = n (A) + n(B) – n (A ∩B)

Probability of at least 5 will have mechanical defect is:

                              = p(  5 mechanical defect  U 6 mechanical defect)

                              = p(5 mechanical defect  ) + p(6 mechanical defect)

                                =(15 C 5 x 10 C1 + 15 C6 X 10C0) / 25 C6

                                = 3003 X 10 / 177100 + 5005 X 1 / 177100

                                = 30030 + 5005 / 177100

                               = 35035 / 177100

                              = 0.1978

0.1978 is the probability that at least 5 keyboards will have mechanical defect.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt