14. More probability Aa Aa An event\'s probability measures the likelihood of it

Question

14. More probability Aa Aa An event's probability measures the likelihood of its occurrence. The probability that an event X occurs is between 0 and 1, inclusive, and is denoted by P(X). If it is impossible for X to occur, then P(X) Rolling a standard six-sided die, the probability of rolling a 7 is zero, P(7)-0. If X is the set of all possible outcomes in the experiment, then X is certain to occur and P(X)1 In the die example, X could be that an integer is rolled, which must occur, and thus P(integer)-1 Otherwise, X is possible but uncertain, and 0

Explanation / Answer

(first part) answer is 1/6.

since there are 6 side of a die and having equal chance to face up so each face will have equal probability=1/6

P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6

(second part) If possible....................called the sample space if you are.....................(P=1/6).

The set of all possible outcomes for an experiment is called a sample space.

(third part) The probability of two mutually exclusive events happening at the same time is zero( 0)

Two events are mutually exclusiveor disjoint if they cannot both occur. One events precludes other.

(fourth part) M=

here number of total outcome or sample space=36

P(M)=18/36=1/2

P(N)=12/36=1/3

P(M and N)= 6/36=1/6

here P(M and N)=P(M)*P(N)

so M and N are inpendents.

M= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) N= (1,3) (1,6) (2,3) (2,6) (3,3) (3,6) (4,3) (4,6) (5,3) (5,6) (6,3) (6,6) M and N= (1,3) (1,6) (3,3) (3,6) (6,3) (6,6)

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