Chapter 11.3, Problem 7LC

Solution

To identify: Theerror did your friend make. The weather forecast for the weekend is a 30% chance of rain on Saturday and a 70% chance is a 100% chance of rain this weekend.

The chance of rain in the weekend is 21%

Given information:

The given is chance of rain on Saturday is 30% and chance of rain on Sunday is 70%

Explanation:

The objective is to find the error in find the chance of rain in the weekend

The friend calculated the percentage as 100%

That means the friend simply added the percentages of chances of rain on Saturday and

Sunday.

But it is wrong to find the chance of rain in the weekend.

Mutually exclusive events:

Mutually exclusive events are those that cannot happen at the same time.

If C and Dare mutually exclusive events

Then

  $\begin{array}{c}P\left(CandD\right)=0\\ P\left(CorD\right)=P\left(C\right)+P\left(D\right)\end{array}$

Independent Events

Independent Events are those in which occurring of one event does not affect occurring of second event

If $C\text{and}D$ are independent event.

Then for independent events

  $\begin{array}{c}P\left(CandD\right)=P\left(C\right)\cdot P\left(D\right)\\ P\left(CorD\right)=P\left(C\right)+P\left(D\right)-P\left(C\right)\cdot P\left(D\right)\end{array}$

The chance of rain occurring on Saturday and the chance of rain occurring on Sunday are not mutually events and they are Independent events.

The chance of rain in the weekend can be calculated as follows

Take $P\left(Saturday\right)=30\%,P\left(Sunday\right)=70\%.$

For independent events, $P\left(CandD\right)=P\left(C\right)\cdot P\left(D\right).$

Substitute the probabilities

  $\begin{array}{c}P\left(SaturdayandSunday\right)=P\left(Saturday\right)\cdot P\left(Sunday\right)\\ =\left(30\%\right)\cdot \left(70\%\right)\\ 21\%\end{array}$

Therefore the chance of rain in the weekend is 21%