Question

Q4) A lottery ticket has a color: Red or Blue followed by one number among 1, 2 and 7.

(a) Specify the sample space for this experiment by listing all possible outcomes.

(b) Let A be the event that the number of the ticket is an odd number, and B be the

event that the color of the ticket is blue. Specify the three events A, B and (A

and B) by listing all the outcomes in each event.

(c) Find the probabilities P(A), P(B) and P(A and B).

(d) Find the probability P(A or B) .

Answer 1

a) here sample space ={Red and 1; Blue and 1 ;Red and 2; Blue and 2 ;Red and 7; Blue and 7 }

b)event in A ={Red and 1; Blue and 1 ;Red and 7; Blue and 7 }

event in B ={Blue and 1 ; Blue and 2 ;Blue and 7 }

event in A and B ={Blue and 1 ; Blue and 7 }

c) P(A) =outcomes in A/outcomes in sample space =4/6 =2/3

P(B)=outcomes in B/outcomes in sample space =3/6=1/2

P(A and B)=outcomes in A and B/outcomes in sample space =2/6=1/3

d)P(A or B)=P(A)+P(B)-P(A and B) =2/3+1/2-1/3 =5/6