Probability Addition Rule Help!!!

**air2slb** · January 29th 2007, 05:56 PM

Will someone please help me work out this problem? I need step by step to understand. Thanks!!!!:

Students in various majors were asked to report their cumulative gpas of 143 math majors 33 refused to respond. Of 175 scoial science majors 59 refused to respond. supposing one of the 318 is selected find the probability of getting a social science major or person who responded? "That was long enough"

**Soroban** · January 30th 2007, 06:06 AM

Hello, air2slb!

You're expected to know this formula:

. . $P(A \lor B) \:=\:P(A) + P(B) - P(A \land B)$

Students in various majors were asked to report their cumulative GPAs.
Of 143 math majors 33 refused to respond.
Of 175 scoial science majors 59 refused to respond.

Supposing one of the 318 is selected.
Find the probability of getting a social science major or person who responded?

Let's organize the information . . .

$\begin{array}{cccc} & \text{refused} & \text{responded} & \text{Totals} \\<br /> \text{math} & 33 & 110 & 143 \\<br /> \text{soc.sc.} & 59 & 116 & 175 \\<br /> \text{Totals} & 92 & 226 & 318 \end{array}$

There are $175$ soc.sc. majors: $P(\text{soc.sc.}) = \frac{175}{318}$

There are $226$ who responded: $P(\text{resp.}) = \frac{226}{318}$

There are $116$ soc.sc major who responded: $P(\text{soc.sc} \land \text{resp.}) = \frac{116}{318}$

Therefore: . $P(\text{soc.sc} \lor \text{resp.}) \:=\:P(\text{soc.sc}) + P(\text{resp.}) - P(\text{soc.sc.} \land \text{resp.})$

. . . . . . . . . . . . . . . . . . . . $= \;\frac{175}{318} + \frac{226}{318} - \frac{116}{318} \;=\;\frac{285}{318} \;=\;\boxed{\frac{95}{106}}$

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