how would i calculate these probabilities, if i'm not given success...?

• Oct 11th 2007, 06:14 PM
beetz
how would i calculate these probabilities, if i'm not given success...?
the problem is as follows: "a student didn't study for a 20 question quiz which has 5 possible answers, and therefore will guess on every question. find each probability-prob. the student gets at least 50% on test, prob. student gets at most 75% on test, and prob. student gets at least a 70% on the test."

well, i know prob right=1/5 and prob wrong= 4/5. so, when setting up my prob. for each part, would pi be .2 because that's success right?
• Oct 11th 2007, 07:13 PM
galactus
The probability the student gets at least a 50% means the student must get at least 10 out of the 20 correct.

The prob. of getting a problem correct is 1/5. Therefore, binomial

at least 50%

$\sum_{k=10}^{20}C(20,k)(\frac{1}{5})^{k}(\frac{4}{ 5})^{20-k}$

The others are analogous to this one.

At most 75%:

$\sum_{k=0}^{15}C(20,k)(\frac{1}{5})^{k}(\frac{4}{5 })^{20-k}$

at least 70%:

$\sum_{k=14}^{20}C(20,k)(\frac{1}{5})^{k}(\frac{4}{ 5})^{20-k}$