Answer to Question #328098 in Statistics and Probability for statistics

Question

1. Consider the following contingency table analyzing the relationship between major and mathematics score.

Column Variables

Row Variables

 

(L)

 (B)

(M)

Natural Sciences (N)

50

80

80

Social Sciences (S)

60

70

80

 

If there is a random selection of one student, determine the following probabilities:

     a. P(N)     b. P(B)     c. P(N Ո L)      d. P(M Ս S)      e.  P(B|N)

Answer 1

$n=50+80+80+60+70+80=420\\a:\\P\left( N \right) =\frac{50+80+80}{420}=0.5\\b:\\P\left( B \right) =\frac{80+70}{420}=0.357143\\c:\\P\left( N\cap L \right) =\frac{50}{420}=0.119048\\d:\\P\left( M\cup S \right) =\frac{60+70+80+80}{420}=0.690476\\e:\\P\left( B|N \right) =\frac{P\left( B\cap N \right)}{P\left( N \right)}=\frac{80/420}{0.5}=0.380952$