Question

You roll a​ six-sided die. Find the probability of each of the following scenarios. ​(a) Rolling a 5 or a number greater than 3. ​(b) Rolling a number less than 5 or an even number. ​(c) Rolling a 2 or an odd number

Answer 1

Explanation:

a.

let A= number 5

B=number >3

P(A)=1/6 {5}

P(B)=3/6 {4,5,6}

p(A∩B)=1/6 {5}

P(AUB)=P(A)+P(B)-P(A∩B)=1/6+3/6-1/6=3/6=1/2

b.

let event C=number<5

D=even number

C=[1,2,3,4}

D={2,4,6}

C∩D={2,4}

P(C)=4/6

P(D)=3/6

P(C∩D)=2/6

P(C∪D)=P(C)+P(D)-P(C∩D)=4/6+3/6-2/6=5/6

c.

let event E=number 2

F= an odd number.

E={2}

F={1,3,5}

E∩F={}

P(E)=1/6

P(F)=3/6

P(E∩F)=0

P(E∪F)=P(E)+P(F)-P(E∩F)=1/6+3/6-0=4/6=2/3