Question

In: Statistics and Probability

Determine if each statement is true or false by dragging labels from below onto the blank...

Determine if each statement is true or false by dragging labels from below onto the blank fields next to the statements.

The probability of the sample space in every experiment is 100%100%. (TRUE/FALSE)

No event can occur with a chance of 110%110%. (TRUE/FALSE)

For any two events EE and FF in an experiment, we have P(E∪F)=P(E)+P(F)P(E∪F)=P(E)+P(F). (TRUE/FALSE)

For every event EE, we have P(E∪Ec)=0P(E∪Ec)=0. (TRUE/FALSE)

For every event EE, we have P(E∩Ec)=0P(E∩Ec)=0. (TRUE/FALSE)

Expert Solution

Solution:

Part 1) The probability of the sample space in every experiment is 100%

Since total probability is 100% and sample space covers all outcomes, hence probability of sample space is always 100%.

Thus this statement is TRUE.

Part 2) No event can occur with a chance of 110%

Since probability never exceed 100%, this statement is FALSE.

Part 3) For any two events E and F in an experiment, we have P(E∪F)=P(E)+P(F)

P(E∪F)=P(E)+P(F) is true only when E and F are mutually exclusive events, otherwise it is:

P(E∪F)=P(E)+P(F) - P(E∩F)

Thus this statement is FALSE.

Part 4) For every event E, we have P(E∪E^c)=0

Since E and E^c are mutually exclusive events, then we have:

P(E∪E^c)= P(E) + P(E^c) which can not be 0.

thus given statement is FALSE.

Part 5) For every event E , we have P(E∩E^c)=0

Since E and E^c are mutually exclusive events, events E and E^c do not occur simultaneously or they do not have common element, hence their intersection is also empty and probability of empty set is always 0.

thus P(E∩E^c)=0 is TRUE.

orchestra answered 2 years ago

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