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) =
Answer:
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