The following table presents the 100 senators of the 113th U.S. Congress on January 3, 2013, classified by political party affiliation and gender.

A senator is selected at random from this group. Compute the following probabilities.

a. The senator is a male Republican.

b. The senator is a Democrat or a female.

c. The senator is a Republican.

d. The senator is not a Republican.

Solution 19E

Step1 of 3:

We have table that presents 100 senators of the 113th U.S. congress on january 3, 2013, classified by political party affiliation and gender.

Male | Female | |

Democrat | 37 | 16 |

Republican | 41 | 4 |

Independent | 2 | 0 |

We need to find,

a).The probability that the senator is a male Republican.

b).The probability the senator is a Democrat or a female.

c).The probability the senator is a Republican.

d).The probability the senator is not a Republican.

Step2 of 3:

a).

We have

Male | Female | Row total | |

Democrat | 37 | 16 | 53 |

Republican | 41 | 4 | 45 |

Independent | 2 | 0 | 2 |

Column total | 80 | 20 | Grand total =100 |

Now, The probability that the senator is a male Republican is given by

P(The senator is a male Republican) = P(MR)

=

=

= 0.41

Hence, P(The senator is a male Republican) = 0.41.

Therefore, The probability that the senator is a male Republican is 0.41.

b).

We have

Male | Female | Row total | |

Democrat | 37 | 16 | 53 |

Republican | 41 | 4 | 45 |

Independent | 2 | 0 | 2 |

Column total | 80 | 20 | Grand total =100 |

The probability the senator is a Democrat or a female is given by

P(The senator is a Democrat or a female) = P(DF)

...