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User Curtis Boylan
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The probability of an event is the chance of the event occuring at all and its usually measured between 0 and 1. if it moves closer to zero, that means the chances are very low and as it moves closer to one, the chances are very high (or quite high).

The probability basically can be calculated as

P (E) = Number of required outcomes / Number of possible outcomes

The number of required outcomes is the expected results from the experiment, in this case the required outcome is the probability or chances of picking a purple marble and a white marble. The number of possible outcomes is the total of all possibilties regardless of whether its part of your expected results or not.

Bowl 1 contains a total of 20 marbles, that means all possible outcomes are 20. There are however 4 purple marbles and that means the required outcomes are 4. Therefore the probabilty of picking a purple marble is calculated as follows;

P(Purple) = No of required Outcomes / No of possible Outcomes

P (Purple) = 4/20

P (Purple) = 1/5

P (Purple) = 0.2

Similarly, the probability or chance of picking a white marble from bowl 2 is calculated as follows;

P(White) = No of required outcomes / No of possible outcomes

P(White) = 6/20

P(White) = 3/10

P(White) = 0.3

At this point we need to know the probability of picking a purple AND a white marble, and this is done each time with replacement. That means the result of one event does not affect the result of the next, they are independent events.

To calculate the probability of independent events, you use the formula

P (Ind Events) = P(A) * P(B)

You multiply both results together, that is the result of the probabilty of event A times that of event B. Our A and B in this case are Purple and White. Therefore,

The probability of picking a purple and a white marble is derived as follows;

P [(W) * (P)] = 0.3 * 0.2

P [(W) * (P)] = 0.06

{Note that you have two decimals, hence your answer will have to be two decimal places}

If the probability of both events is derived as 0.06, then she has a 6% chance of drawing a purple marble from bowl 1 and a white marble from bowl 2. This can be used as a predictor, that is if she now draws both marbles from both bowls 200 times, the result predictably would be;

Prediction = Probability * Number of experiments

Prediction = 0.06 * 200

Prediction = 12

User Tomasita
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