A fair coin is tossed three times and the events AA, BB, and CC are defined as follows: A:{A:{ At least one head is observed }} B:{B:{ At least two heads are observed }} C:{C:{ The number of heads observed is odd }} Find the following probabilities by summing the probabilities of the appropriate sample points (note that 0 is an even number):

This question is incomplete, the complete question is;

A fair coin is tossed three times and the events AA, BB, and CC are defined as follows: A:{A:{ At least one head is observed }} B:{B:{ At least two heads are observed }} C:{C:{ The number of heads observed is odd }} Find the following probabilities by summing the probabilities of the appropriate sample points (note that 0 is an even number): a) P(B) =, b) P(A or B) =

a) probability of B is 0.5

b) probability of (A or B)  is 0.875

Step-by-step explanation:

Given the data in the question;

The coin is tossed 3 times.

so let S represent the sample space with the probabilities;

S = [ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT ]

so n(S) = 8

now let A be the set where at least one head is observed;

A = [ HHH, HHT, HTH, THH, HTT, THT, TTH, ]

n( A) = 7

let B be the set where at least two head is observed;

B = [ HHH, HHT, HTH, THH, ]

n(B) = 4

let C be the set where number of heads are odd;

C = [ HHH, HTT, THT, TTH ]

n(C) = 4

so

a) P(B) = ?

probability of B will be;

P(B) = n(B) / n(S)

we substitute

P(B) = 4 / 8 = 0.5

Therefore, probability of B is 0.5

b) P(A or B) = ?

the favorable number of cases to event A∪B is

A∪B = [ HHH, HHT, HTH, THH, HTT, THT, TTH, ]∪[ HHH, HHT, HTH, THH, ]  

A∪B = [ HHH, HHT, HTH, THH, HTT, THT, TTH, ]

n(A∪B) = 7

Now the probability of A or B will be

P( A∪B ) = n(A∪B) / n(S) = 7/8 = 0.875

Therefore, probability of (A or B)  is 0.875

i can answer this question sweetie!

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.