To announce the winner of a contest, Maria draws from a bowl of raffle

Question

To announce the winner of a contest, Maria draws from a bowl of raffle tickets numbered 1 through 60. What is the probability that the winning number is either even or divisible by 3?

A. 1/2
 
B. 2/3
 
C. 3/4
 
D. 4/5
 
E. 5/6

ScottTargetTestPrep · Accepted Answer

To find the number of multiples of an integer x in a given interval, we use the formula: (greatest multiple of x - smallest multiple of x)/x + 1

The number of multiples of 2 from 1 to 60, inclusive, is (60 - 2)/2 + 1 = 30.

The number of multiples of 3 from 1 to 60, inclusive, is (60 - 3)/3 + 1 = 20.

We have double-counted the integers that are multiples of both 2 and 3, so we need to subtract out the number of multiples of both 3 and 2 (or the number of multiples of 6).

The number of multiples of 6 from 6 to 60, inclusive, is (60 - 6)/6 + 1 = 10.

Thus, the probability of picking a raffle ticket that is either an even number or a multiple of 3 is (30 + 20 - 10)/60 = 40/60 = 2/3.

Answer: B

u1983 · Answer

even(A)=30
Div by 3(B)=20
 even and div by 3 (A and B) = 10
A or B = A + B - (A and B) = 40
HENCE, P(A or B) =40/60= 2/3------------B

pushpitkc · Answer

There are a total of 30 even integers in the bowl of raffle tickets.
Also, there are 20 integers which are divisible by 3(out of which 
3,9,15,21,27,33,39,45,51,57 are odd and 6,12,18,24,30,36,42,48,54,60 are even)

Since there is an overlap of 10 even integers in both the lists, the total 
number of raffle tickets which are either even or divisible by 3 are 30+20-10 = 40

Therefore, the probability that Maria draws the winning number is  \frac{40}{60} = \frac{2}{3}  (Option B)

asthagupta · Answer

even elements=30
Elements Divisible by 3 =20
common elements i.e. elements which are both even and div by 3 = 10
so total elemtns that are even or divisible by 3:= 30+20-10=40

P =  \frac{40}{60}  =  \frac{2}{3}

B it is

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To announce the winner of a contest, Maria draws from a bowl of raffle

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