I don't know how I got the answer for this binomial probability question! (The answer is correct but I don't understand my working out) (1 Viewer)

[okeydonkey]

For this question, my original working out gave me a result that was greater than 1 which was obviously wrong for probability so I sort of guesstimated the working out and finally got the answer but I don't understand the logic behind this working out (assuming that my working out is right. If it is wrong then I don't know what to say lol)

Steel rods are manufactured to be 4cm in diameter but they are acceptable if they are between 3.98cm and 4.02cm. The manufacturer finds that in the long run 3% are rejected as oversized and 3% are rejected as undersized. A random sample of 10 rods is selected from the population. What is the probability that it contains no more than one which has to be rejected (to 4 decimal places)? (final answer is 0.8824)

The working out that gave me the answer is P=0.94^10 + 2*0.3*0.94 = 0.8824

However, I don't understand why for the second part (2*0.3*0.94), it is not multiplied by 10. When choosing a rejected rod from the sample, there are 10 chances that out of those 10 rods, 1 rod will be oversized or undersized. However, if I do that, I will get an answer that is over 1. I don't quite understand the answer. Could someone please explain this to me? Thank you!

 

[Drongoski]

P(reject) = 0.03 + 0.03 = 0.06
P(accept) = 1 - P(reject) = 1 - 0.06 = 0.94



There are 11 terms in this binomial expansion, corresponding to i =0, 1, 2 . . . 10
P(none rejected) = P(when i=0) and P(1 rejected) = P(when i = 1)
P(at most 1 is rejected in 10) = P(0 rejected) + P(1 rejected)

=

= 0.5386... + 0.34379...

= 0.8824

 

[catha230]

P(reject) = 0.03 + 0.03 = 0.06
P(accept) = 1 - P(reject) = 1 - 0.06 = 0.94

Hi how do you get the answer above? Could you please elaborate more on this?

 

[Drongoski]

Fully elaborated, and beautifully explained, above.
Being a slow coach, and not being sure which TeX codes to use, I was entering a couple of lines at a time.

Sorry: I did not see the missing part (now rectified) in line 3.

 

[okeydonkey]

Fully elaborated, and beautifully explained, above.
Being a slow coach, and not being sure which TeX codes to use, I was entering a couple of lines at a time.

Thank you so much for the help!