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There are 2 decks of cards. The first deck has a 100 cards labelled...

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Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
was time consuming to find number of multiples in two intervals

1-100: 98-7/7+1=14

101-250: 245-105/7+1=21

14/100*21/150=2*7*3*7/15000=7^2*6/15000=7^2/2500

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Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
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kdatt1991 wrote:
There are 2 decks of cards. The first deck has a 100 cards labelled with integers from 1 to 100. The second one has 150 cards labelled with integers 101 to 250. If we select one card at random from each deck, what is the probability that numbers on both selected cards will be multiples of 7?

A. $$\frac{7}{3000}$$

B. $$\frac{7}{2500}$$

C. $$\frac{7^2}{15000}$$

D. $$\frac{7^2}{7500}$$

E. $$\frac{7^2}{2500}$$

Could someone please explain the answer to this question. It will be much appreciated, thank you

Multiples of 7 in 1 - 100:
7, 14, ..., 98
7*1 to 7*14 (= 98) gives us 14 multiples.

Multiples of 7 in 101 - 250
105, 112, ..., 245
7*15 (=105) to 7*35 (= 245) gives us 35 - 15 + 1 = 21 multiples

Probability of picking a multiple of 7 in both cases = (14/100) * (21/150) = 7^2/2500

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Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
kdatt1991 wrote:
There are 2 decks of cards. The first deck has a 100 cards labelled with integers from 1 to 100. The second one has 150 cards labelled with integers 101 to 250. If we select one card at random from each deck, what is the probability that numbers on both selected cards will be multiples of 7?

A. $$\frac{7}{3000}$$

B. $$\frac{7}{2500}$$

C. $$\frac{7^2}{15000}$$

D. $$\frac{7^2}{7500}$$

E. $$\frac{7^2}{2500}$$

Let’s determine the number of multiples of 7 from 1 to 100 and from 101 to 250.

From 1 to 100: (Note that the greatest multiple of 7 is 98 and the smallest multiple of 7 is 7.)

(98 - 7)/7+ 1 = 91/7 + 1 = 14

From 101 to 250: (Note that the greatest multiple of 7 is 245 and the smallest multiple of 7 is 105.)

(245 - 105)/7+ 1 = 140/7 + 1 = 21

Thus, the probability of selecting a multiple of 7 in the first set of cards is 14/100, and in the second set it is 21/150. We want the probability that both selected cards will contain multiples of 7, so we multiply the two probabilities to determine the total probability: 14/100 x 21/150 = (14 x 21)/(100 x 150) = (7 x 7)/(50 x 50) = 7^2/2500.

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Re: There are 2 decks of cards. The first deck has a 100 cards labelled... [#permalink]
From 1 to 100: (Note that the greatest multiple of 7 is 98 and the smallest multiple of 7 is 7.)
=> (98 - 7)/7+ 1 = 91/7 + 1 = 14 multiples of 7

From 101 to 250: (Note that the greatest multiple of 7 is 245 and the smallest multiple of 7 is 105.)
=> (245 - 105)/7+ 1 = 140/7 + 1 = 21 multiples of 7

Thus, The probability of selecting a multiple of 7 in the first set of cards is 14/100, and in the second set it is 21/150.

Now, The probability that both selected cards will contain multiples of 7,
so we multiply the two probabilities to determine the total probability: 14/100 x 21/150 = (14 x 21)/(100 x 150) = (7 x 7)/(50 x 50) = 7^2/2500.