91Ó°ÊÓ

The following table shows the age distribution of senators in the United States Congress as of Fall 2013.

A = event the senator is under 50,

B = event the senator is in his or her 50s,

C = event the senator is in his or her 60s, and

S = event the senator is under 70.

Formula that was used:

Probability of event =$\frac{No.offavourableoutcomes}{Totalno.ofoutcomes}$

Total No. of outcomes =$11+30+37+20+2=100$

A favourable number of outcomes for event S =$11+30+37=78$

$P\left(S\right)=\frac{78}{100}=0.78$

Using the table and f/N rule the value of P(s) is$0.78$

A = event the senator is under 50,

B = event the senator is in his or her 50s,

C = event the senator is in his or her 60s, and

S = event the senator is under 70.

The event S in terms of events A, B, and C can be calculated using the following information:

$S=(AorBorC)$

Total no. of outcome $=100$

role="math" localid="1651320094416" $$\begin{gathered} P\left(A\right)=\frac{11}{100}=0.11 \\ P\left(B\right)=\frac{30}{100}=0.3 \\ P\left(C\right)=\frac{37}{100}=0.37 \end{gathered}$$

A = event the senator is under 50,

B = event the senator is in his or her 50s,

C = event the senator is in his or her 60s, and

S = event the senator is under 70.

$$\begin{gathered} P\left(S\right)=P\left(A\right)+P\left(B\right)+P\left(C\right) \\ 0.11+0.3+0.37=0.78 \end{gathered}$$

Because occurrences A, B, and C are mutually exclusive, the result corresponds to portion (a).