Question

Alexander has a bag that contains pineapple chews, cherry chews, and watermelon chews. He performs an experiment. Alexander randomly removes a chew from the bag, records the result, and returns the chew to the bag. Alexander performs the experiment 40 times. The results are shown below:
A pineapple chew was selected 8 times.
A cherry chew was selected 11 times.
A watermelon chew was selected 21 times.

Based on these results, express the probability that the next chew Alexander removes from the bag will be cherry chew as a percent to the nearest whole number.

Answer 1

SOLUTION

GIVEN

Alexander has a bag that contains pineapple chews, cherry chews, and watermelon chews. He performs an experiment. Alexander randomly removes a chew from the bag, records the result, and returns the chew to the bag. Alexander performs the experiment 40 times. The results are shown below:

A pineapple chew was selected 8 times.

A cherry chew was selected 11 times.

A watermelon chew was selected 21 times.

TO DETERMINE

Based on these results, express the probability that the next chew Alexander removes from the bag will be cherry chew as a percent to the nearest whole number.

EVALUATION

Alexander performs the experiment 40 times.

So total number of possible outcomes = 40

Let A be the event that the next chew Alexander removes from the bag will be cherry chew

It is given that a cherry chew was selected 11 times.

So total number of possible outcomes for the event A is 11

Hence the required probability

$\displaystyle\sf{ = \frac{Number \: of \: favourable \: cases \: for \: A }{Total \: number \: of \: possible \: outcomes } }$

$\displaystyle\sf{ = \frac{11}{40} }$

Now expressing as a percent to the nearest whole number

$\displaystyle\sf{ = \frac{11}{40} \times 100\% }$

$\displaystyle\sf{ = 27.5\% }$

$\displaystyle\sf{ \: \approx \:28\% }$

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