# Find the indicated probability?

• Oct 5th 2009, 08:58 PM
Almondzqueen
Find the indicated probability?

A)The quiz consists of 10 true/false questions. To pass the quiz Judy must answer at least 7 questions correctly. But if Judy guesses on each question, what is the probability that she will pass the quiz?

B)The multiple choice exam has 10 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the exam, guesses on all questions, what is the probability
that she will answer exactly 3 questions correctly?

So I remember the answer for the first part being .172 but need help knowing how to get that answer. iTS followup question only confuses me more. (Headbang)
Help would truly be appreciated...
• Oct 5th 2009, 09:35 PM
Rapha
Hello Almondzqueen!

Quote:

Originally Posted by Almondzqueen

A)The quiz consists of 10 true/false questions. To pass the quiz Judy must answer at least 7 questions correctly. But if Judy guesses on each question, what is the probability that she will pass the quiz?

B)The multiple choice exam has 10 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the exam, guesses on all questions, what is the probability
that she will answer exactly 3 questions correctly?

So I remember the answer for the first part being .172 but need help knowing how to get that answer. iTS followup question only confuses me more. (Headbang)
Help would truly be appreciated...

You should use the binomial distribution.

A) There are 10 question, you need to guess the right answer for 7 question. So. $\displaystyle \begin{vector} 10 \\ 7 \end{vector}$

This are true/false questions, so there are two possibilities for each question. The probabilty to choose the right answer therefore is 0.5; to choose the wrong answer is 0.5, too.

Using the binomial distribution:

prob("exactly 7 questions right")
$\displaystyle \begin{pmatrix} 10 \\ 7 \end{pmatrix}*0.5^7*0.5^{10-7}$

$\displaystyle =\begin{pmatrix} 10 \\ 7 \end{pmatrix}*0.5^7*0.5^{3}$

You pass the test, if you answer 8, 9 and 10 questions correctly. Do you know how to find this probs on your own?

After that you need to sum all probabilities.

B) It is the same distribution, same formula, similar problem
10 questions, you want to solve
But there are 4 possible answers, 3 of them are wrong, 1 is right.
So choosing the right one: 1/4 = .25
choosing the wrong answer: 3/4 = 0.75

Binomial distribution:

$\displaystyle \begin{pmatrix} 10 \\ 3 \end{pmatrix}*0.25^3*0.75^{10-3}$

B) It is the same distribution, same formula, similar problem
10 questions, you want to solve
But there are 4 possible answers, 3 of them are wrong, 1 is right.
So choosing the right one: 1/4 = .25
choosing the wrong answer: 3/4 = 0.75

Binomial distribution:

$\displaystyle \begin{pmatrix} 10 \\ 3 \end{pmatrix}*0.25^3*0.75^{10-3}$

$\displaystyle =\begin{pmatrix} 10 \\ 3 \end{pmatrix}*0.25^3*0.75^{7}$

Do you understand?

kind regards
Rapha