20-Q mult.-choice test, 5 choices/Q: find prob of 15 right

[MRS.FREE]

20-Q, mult.-choice exam w/ 5 ans. for each Q. Find prob. of

I HAVE GONE THROUGH THE CHAPTER AND TAKEN ALL MY NOTES, WENT OVER ALL OF THE EXAMPLES IN THE BOOK BUT I CAN NOT FIGURE OUT HOW TO GET THESE SET UP AND WORKED OUT. CAN SOMEONE PLEASEEEE HELP ME!?!? I REALLY APPRECIATE IT! :?

A STUDENT TAKES A 20 QUESTION, MULTIPLE CHOICE EXAM WITH FIVE CHOICES FOR EACH QUESTION AND GUESSES ON EACH QUESTION. FIND THE PROBABILITY OF GUESSING AT LEAST 15 OUT OF 20 CORRECTLY. WOULD YOU CONSIDER THIS EVENT TO BE LIKELY OR NOT, AND WHY?

N=
P=
X=
P(15)=
IS THIS LIKELY TO OCCURE?- WHY?


APPROXIMATLY 10.3% OF AMERICAN HIGH SCHOOL STUDENTS DROP OUT OF SCHOOL BEFORE GRADUATION. CHOOSE 10 STUDENTS ENTERING HIGH SCHOOL AT RANDOM. FIND THE PROBABILITY THAT:
A) no more than 2 drop out

N=
P=
Q=
X=

b) at least 6 graduate *(WHICH IS THE SAME AS P(AT MOST 5 DROP OUT)

N=
P=
Q=
X=

c) all 10 stay in school and graduate *(WHICH IS THE SAME AS NONE DROP PUT)

N=
P=
Q=
X=


THE PERCENTAGE OF COUPLES WHERE BOTH PARTIES ARE IN THE LABOR FORCE IS 52.1. CHOOSE 5 COUPLES AT RANDOM. FIND THE PROBABILITY THAT:
A) NONE OF THE COUPLES HAVE BOTH PERSONS WORKING

N=
P=
Q=
X=

B) MORE THAN 3 OF THE COUPLES HAVE BOTH PERSONS IN THE LABOR FORCE

N=
P=
Q=
X=

C) FEWER THAN 2 OF THE COUPLES HAVE BOTH PARTIES WORKING

N=
P=
Q=
X=

 

[soroban]

Re: 20-Q, mult.-choice exam w/ 5 ans. for each Q. Find prob. of

Hello, MRS.FREE!

These are standard problems in a section called "Independent Events" or "Binomial Probability. ".
It's hard to believe that a book would assign them without giving the formula, at least.

These are all the same type.
I'll do that last one; it's the simplest.

And take off your CAPS LOCK.

The percentage of couples where both parties work is 52.1%.
Choose 5 couples at random.
Find the probability that:

A) none of the couples have both parties working.

\(\displaystyle \begin{array}{ccccc}P(\text{both working}) &=&P(B) &=&0.521 \\ P(\sim\text{both working}) &=&P(N) &=& 0.479 \end{array}\)


\(\displaystyle \text{"None have both working" means: }\,0 B,\,5 N\)

\(\displaystyle P(0B,\,5N) \:=\:{5\choose0}(0.521)^0(0.479)^5 \:=\:0.92521608\)

B) More than 3 of the couples have both paraties working.

\(\displaystyle \text{"More than 3B" means: }\4B,1N),\;(5B,0N)\)

\(\displaystyle \begin{array}{ccccc}P(4B,1N) &=& {5\choose4}(0.521)^4(0.479)^1 &=& 0.176464118 \\ \\[-3mm] P(5B,0N) &=& {5\choose5}(0.521)^5(0.479)^0 &=& 0.938387303 \end{array}\)

\(\displaystyle \text{Therefore: }\(4B\text{ or }5B) \;=\;0.176464118 + 0.038387393 \;=\;0.214851511\)

C) fewer than 2 of the couples have both parties working.

\(\displaystyle \text{"Fewer than 2B" means: }\0B,5N)\,\text{ or }\,(1B,4N)\)

\(\displaystyle \begin{array}{ccccc}P(0B,5N) &=& {5\choose0}(0.521)^0(0.479)^5 &=& 0.025216080 \\ P(1B,4N) &=& {5\choose1}(0.521)^1(0.470^4 &=& 0.137135464 \end{array}\)

\(\displaystyle \text{Therefore: }\(0B\text{ or }1B) \;=\;0.025216080 + 0.137135464 \;=\;0.162351544\)

 

[MRS.FREE]

all the other problems were to be set up similar but htis one is diff and i don't even know where to start. can someone please help me????

a student takes a 20 question multile choice exam with five choices for each question and guesses on each question. find th probabulity of guessing at least 15 out of 20 correctly. would u consider this event to be likely to occur?

im going out on a limb here to see if i can figure this out, am i way off????
n= i think its 20
p= is it .2 (same as one fith) ?
x= 15 (right)
p(15)= 20!/5!15! = (15504)(.2) to the fifteenth (.8) to the fifth= .000000166? that doesnt look right????

thank you for your help!