Question

13. [3] You shuffle a deck of playing cards and the chance you get a diamond card is 0.25. You repeat this process 200 times, putting the card back each time, and out of those 200 attempts you get 57 diamond cards. This demonstrates a. The law of large numbers b. The law of averages 14. [3] You shuffle a deck of playing cards and the chance you get a diamond card is 0.25. You repeat this process times, putting the card back each time, and out of those five attempts you get five diamond cards. You comment, "Okay the chance of getting a diamond card again will be lower than 25%." This statement demonstrates what is meant by a. The law of large numbers b. The law of averages 15. (3) You are told that P(A) = 0.72 P(B) = 0.15 and that the events are disjoint. What is the probability of PIA AND B)? 16. [3] You are told that P(A) = 0.45 P(B) = 0.20 and that the events are independent. What is the probability of PIA OR B)? 17. [3] True or False - If two events are independent, then the two events must be disjoint.

Answer 1

The law of large numbers describes the result of performing the same experiment a large number of times ,so that the average of the results obtained from. A large number of trials should be close to the expected value and will tend to become closer to the expected value as the number of trials increases.

Where as the law of averages is a belief that a certain event over a period of time will occur at a frequency that is similar to it's probability. Like believing that if 3 flips of coins resulted in heads, the next flip will be tail.

So considering the above definitions.

13- law of large numbers.

14- law of averages.

15- two events are called disjoint if they cannot happen together. That means in this scenario there is no possibility of A and B happening together , i.e probability of their intesection P(A and B) =0

16- if the events are independent then the probability of their intesection is equal to product of their individual probabilities.

i.e p(A and B) = p(A) p(B) .

Since p(A Or B) = p(A) + p(B) - p(A and B)

= p(A) + p(B) - p(A) p(B)

= 0.45+0.20-(0.45×0.20)

= 0.56

17- let A and B be two events, so if the events are disjoint we have

P(A and B) = 0 (explained above)

And if the two events are independent then

P(A and B) = p(A) p(B)

So two events are independent doesn't mean they are disjoint. The statement is false.