# Math Help - How to figure out (at least) probability in Statistics?

1. ## How to figure out (at least) probability in Statistics?

What is the probability that a student will answer at least two questions correctly by random guessing on an exam with 8 multiple-choice questions each of which as three options?

What I don't get is the at least two questions correctly part. Do they mean P(2) + P(3) + P(4) +P(5) + P(6) + P(7) + (P8)?
P(2) means 8C2 x (1/3)^2(2/3)^6 and ect....

2. At least one is the oppsite of none: $1-P(none)$

3. So what do they want you to do when they say at least two?

4. The answer I came up with is 0.804907788. Can anybody confirm that I did it correctly?

5. Hello, krzyrice!

The answer I came up with is 0.804907788.
Can anybody confirm that I did it correctly?

I did it by using the "opposite" approach.
The opposite of "at least two" is "less than two" (zero or one).

$P(0) \:=\:_8C_0(\tfrac{1}{3})^0(\tfrac{2}{3})^8 \:=\:0.039018442
$

$P(1) \:=\:_8C_1(\tfrac{1}{3})^1(\tfrac{2}{3})^7 \:=\:0.156073769
$

. . Hence: . $P(0\text{ or }1) \:=\:0.039018492 + 0.156073769 \:=\:0.195092211$

Therefore: . $P(\text{at least 2}) \;=\;1-0.195092211 \;=\;0.804907789$

6. Thank you so much for your help! You are a great mathematician and now I have more confidence in getting that A on the test tomorrow.