Question

Let an integer be chosen at random from the integers 1 to 30 inclusive. Find the probability that the integer chosen is divisible by 4 or is greater than 25 and less than 30.

Answer 1

A:4*7=28. so there are 7 multiples upto 30. P(A)=7/30
B:26,27,28,29 i.e. 4 numbers satisfy the 2nd criteria. P(B)=4/30

P(A∩B)=1/30 (since 28 belongs to both A&B)

P(A∪B)= P(A)+P(B)-P(A∩B)= (7+4-1)/30= 1/3

Answer 2

Hence, the required probability is:

1/3

Explanation:

Let A denote the event that the integer chosen is divisible by 4.

i.e. A={4,8,12,16,20,24,28}

Hence, P(A)=7/30

and B denote the event that the integer is greater than 25 and is less than 30.

i.e. B={26,27,28,29}

Hence, P(B)=4/30

Hence, A∩B denote the event that the integer us divisible by 4 and is greater than 25 and is less than 30.

i.e. A∩B={28}

Hence, P(A∩B)=1/30

and A∪B denote the event that the integer chosen is divisible by 4 or is greater than 25 and less than 30.

Hence,we know that:

P(A∪B)=P(A)+P(B)-P(A∩B)

i.e. P(A∪B)=7/30+4/30-1/30

P(A∪B)=10/30

P(A∪B)=1/3