For this question, I got the exact same equation to find roots and then I eliminated the 3rd option as it is above one as well.
According to the quiz, the correct answer is D
But, we are given the probability of when event happens 3 times, when I take either of the two values and substitute, I get 0.711 as the right choice that gives me a 0.3 . So that means P is greater. So how is answer choice D ?
I don’t understand what you mean.
So you have that p could be either approximately be 0.481 or 0.711, hence the answer is D because these numbers lie on both sides of \frac 12.
I am saying, I substituted the those values in the exactly 3 probability equation and 0.711 matches the 0.3 already given. So wouldnt Option A be the correct answer
The equation for an event happening exactly 3 times would be 0.3 = P(X = 3) = {5 \choose 3} p^3 (1-p)^2 and so you arrive at:
p^5 - 2p^4 + p^3 - 0.03 = 0
The roots of this quintic equation are the values of p that could work given that they’re 0 \leq p \leq 1.
Out of the three real roots, you eliminated the one out of bounds for the correct reason. However, the two values of p which you’re left with both work — which is why the answer is D bc of their relative position from 1/2 (the roots are greater/less than 1/2).
I’m not sure what you’re substituting bc as u can see there’s no substitution happening here.
Thank you! I get it now.
I think what I had done is take the values and resubstitute it to find P that matches 0.3
