Question

The crackers in a box have three shapes. Max randomly choose one cracker at a time 40 times, returning the cracker to the box each time.Crackers (Shape/frequency)Oval: 18Rectangle: 14Star: 8Find the experimental probability of choosing a cracker that is not star-shaped.

Answer 1

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There are 3 shapes of crackers in the box, oval, rectangular and star. Max took one cracker at a time, 40 times, recorded its shape and put it back in the box.

To calculate the experimental probability of getting each shape, you have to divide the number of times he got that determined shape (frequency of the cracker shape) by the total number of times he repeated the experiment.

So for the oval crackers, the probability will be:

`P(oval)=\frac{\text{frequency}}{\text{Total}}=(18)/(40)=0.45`

For the rectangular crackers the probability will be

`P(rec\tan gular)=\frac{\text{frequency}}{\text{Total}}=(14)/(40)=0.35`

For the star-shaped crackers the probability will be:

`P(star)=\frac{\text{frequency}}{\text{Total}}=(8)/(40)=0.20`

Now you have to determine the probability of the event "NOT star shaped" this occurs when you get either rectangular or oval shaped crackers. This event is complementary to the event "Star shaped" and you can calculate it as:

`\begin{gathered} P(Star^c)=1-P(Star) \\ P(Star^c)=1-0.20 \\ P(Star^c)=0.80 \end{gathered}`

You have to express it as a percentage so multiply the result by 100

`0.80\cdot100=80`

The experimental probability of not geting a star shaped cracker is 80%

Done!

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