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

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Math Expert
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To announce the winner of a contest, Maria draws from a bowl of raffle  [#permalink]

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14 Mar 2018, 21:25
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:26) correct 34% (01:40) wrong based on 70 sessions

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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

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Re: To announce the winner of a contest, Maria draws from a bowl of raffle  [#permalink]

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14 Mar 2018, 21:46
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
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Re: To announce the winner of a contest, Maria draws from a bowl of raffle  [#permalink]

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14 Mar 2018, 23:32
Bunuel wrote:
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

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)
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Re: To announce the winner of a contest, Maria draws from a bowl of raffle  [#permalink]

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15 Mar 2018, 00:26
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 = $$\frac{40}{60}$$ = $$\frac{2}{3}$$

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Re: To announce the winner of a contest, Maria draws from a bowl of raffle  [#permalink]

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19 Mar 2018, 06:41
1
Bunuel wrote:
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

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.

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Re: To announce the winner of a contest, Maria draws from a bowl of raffle  [#permalink]

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17 Sep 2019, 14:20
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Re: To announce the winner of a contest, Maria draws from a bowl of raffle   [#permalink] 17 Sep 2019, 14:20
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