Question

A bag consist of 4 blue marbles and 6 red marbles. Three marbles are randomly selected from the bag with replacement after each selection. Twenty five trials are conducted and the results are given by the table. Compare the theoretical and experimental probabilities for the compound event: red marble, red marble, red marble


A) The theoretical and experimental probabilities are equal. B) The event occurred 0.07 more than theoretically expected. C) The event occurred 0.14 less than theoretically expected.  D) The event occurred 0.14 more than theoretically expected.

Answer 1

The probability of picking a red marble three times in a row with replacement is:

number of red marbles divided by total number of marbles cubed...

(6/10)^3=27/125

The above is the theoretical probability...

From the chart we see that three reds in a row happened twice in twenty-five trials so the experimental probability is:

2/25

The experimental probability about 0.14 less than theoretically expected...

C)

Answer 2

Option C is right

Explanation:

With replacement 3 marbles are drawn

Since there are 4 blue marbles and 6 red marbles, probability of drawing a red marble = 0.6

Since with replacement this probability p = 0.6 remains the same

Hence probability of drawing all 3 red = 0.6^3 =0.216

Real experiments table show that out of 25 trials only 2 successes were seen. i.e. 3 red balls drawing occurred only 2 times

Hence experimental probability =2/25 =0.08

The difference between theoretical probability = 0.216-0.08 = 0.136

=0.14 apprxy.

Thus we find that the event occurred 0.14 times less than theoretically expected.