Check all the statements that are true If A and B are mutual

Check all the statements that are true: If A and B are mutually exclusive events, the probability for the event (A and B) is zero. The probability for an event may be zero. If a random experiment has n possible outcomes, then there are exactly 2^n many events associated with the random experiment. In probability theory, an event is one possible outcome of an experiment. If an experiment has n possible outcomes, each outcome has probability 1/n. If an event has a probability of 50%, then, if the random experiment is carried out 100 times, it is unlikely, though not impossible, that the event will occur less than 10 times. If event A has probability p_1 and event B has probability p_2, then the event (A or B) has probability p_1 + p_2. If an event has a probability of 50%, then, if the random experiment is carried out 10 times, the event will occur exactly 5 times. If A and B are different events, the probability for the event (A and B) is zero. The probability for an event may be larger than 1.

Solution

Dear Student

Thank you for using Chegg !!

A) Mutually exclusive events are defined as The events which cannot occur together.

Since the two events are mutually exclusive, then the probability of them occuring together is 0.

Hence given statement is TRUE>

B) The probabiity of any even is always determined between 0 & 1 both inclusive. where ) is the probability for an impossible event and 1 is the probability for a sure event.

Hence the given statement that an even can have probability as 0 is TRUE.

C) Number of events is always given by 2^ (Number of possible outcomes) for an experieme. Hence TRUE.

D) Please note that An event is a subset of a sample space. An event with only one possible outcome is a simple event. If an event equals the sample space, then the event is a certain event.

Hence the given statement is FALSE.

PS:- Kindly note at chegg we have a policy of answering maximum 4 sub parts of a question Thank you !!