# Calculating Probabilities from a Table

Classified in Mathematics

Written at on English with a size of 2.5 KB.

## Worksheet: Revisiting Calculating Probabilities from a Table

### 1. Goals

G: Grades | P: Popular | S: Sports | Totals | |
---|---|---|---|---|

B: Boy | 117 | 50 | 60 | 227 |

F: Girl | 130 | 91 | 30 | 251 |

Totals | 247 | 141 | 90 | | 478 |

P(F) = 251/478 = 0.525

The probability that a randomly selected student is a girl is 0.525.

P(P^{C}) = (247 + 90)/478 = (478 – 141)/478 = 337/478 = 0.705

The probability that a randomly selected student did not indicate being popular as a primary goal is 0.705.

P(B or S) = (227 + 90 – 60)/478 = 257/478 = 0.538

The probability that a randomly selected student is a boy or indicated a primary goal is to excel at sports or both is 0.538.

P(B and S) = 60/478 = 0.126

The probability that a randomly selected student is a boy and indicated a primary goal is to excel at sports is 0.126.

P(S|B) = 60/227 = 0.264

The probability that a randomly selected student indicated a primary goal is to excel at sports given that the selected student is a boy is 0.264.

P(G|F) = 130/251 = 0.518

The probability that a randomly selected student indicated a primary goal is good grades given that the selected student is a girl is 0.518.

e. i. (251/478)(250/477)(249/476)(248/475)(247/474) = 0.039 ii. (247/478)(246/477)(245/476)(244/475)(243/474) = 0.036

### 2. Highest Education

Less than High School | High School | More than High School | Totals | |
---|---|---|---|---|

Better off | 140 | 450 | 420 | 1010 |

Same | 60 | 250 | 110 | 420 |

Worse off | 200 | 300 | 70 | 570 |

Totals | 400 | 1000 | 600 | | 2000 |

- 450/1000 = 0.450
- 1010/2000 = 0.505
- (400/2000)(399/1999)(398/1998) = 0.008
- 450/2000 = 0.225
- 420/1010 = 0.416
- (1010 + 570)/2000 = (2000 – 420)/2000 = 1580/2000 = 0.79
- (570/2000)(569/1999)(568/1998)(567/1997) = 0.007
- (570 + 1000 – 300)/2000 = 1270/2000 = 0.635