# Word problem

• Sep 8th 2009, 02:37 PM
javax
Word problem
I need some help and clarifications on such problems. For example:

A student thinks he will succeed on subjects "Probability", "Statistics" and in both of them with the probabilities 0.7, 0.6 and 0.5 respectively. Find the probabilities:
1). p1: The student will succeed at least in one of the subjects
2), p2: The student will succeed only in one of the subjects
3), p3: The student will succeed not more than in one subject
result: p1 = p2+p3

:)
• Sep 8th 2009, 02:46 PM
Plato
Quote:

Originally Posted by javax
I need some help and clarifications on such problems. For example:

A student thinks he will succeed on subjects "Probability", "Statistics" and in both of them with the probabilities 0.7, 0.6 and 0.5 respectively. Find the probabilities:
1). p1: The student will succeed at least in one of the subjects
2), p2: The student will succeed only in one of the subjects
3), p3: The student will succeed not more than in one subject

$\displaystyle p_1=P(P)+P(S)-P(B)$
$\displaystyle p_2=P(P)+P(S)-2P(B)$
$\displaystyle p_3=1-P(B)$
• Sep 8th 2009, 02:49 PM
javax
Quote:

Originally Posted by Plato
$\displaystyle p_1=P(P)+P(S)-P(B)$
$\displaystyle p_2=P(P)+P(S)-2P(B)$
$\displaystyle p_3=1-P(B)$

ok thanks, would you please explain how you derived formulas for p2 and p3?
• Sep 8th 2009, 03:08 PM
Plato
Quote:

Originally Posted by javax
ok thanks, would you please explain how you derived formulas for p2 and p3?

Exactly one:
$\displaystyle p_2=P\left( {A \cap B^c } \right) + P\left( {A^c \cap B} \right) =$$\displaystyle \left[ {P(A) - P\left( {A \cap B} \right)} \right] + \left[ {P(B) - P\left( {A \cap B} \right)} \right] = \left[ {P(A) + P(B) - 2P\left( {A \cap B} \right)} \right]$

$\displaystyle p_3$ is "No more than one" is "not both".