Shalini Suresh wrote:There are 2 decks of 10 cards each numbered from 11 to 20 inclusive. If we pick a card from each pile, what is the probablity that the product of the numbers picked is divisible by 6?
A)0.23
B)0.36
c)0.40
D)0.42
E)0.46
Answer is D
Request someone to explain .
Total number of products:
Number of options from deck 1 = 10.
Number of options from deck 2 = 10.
To combine these options, we multiply:
10*10 = 100.
Multiples of 6:
For the product to be a multiple of 6, it must be a divisible by 2 and 3.
Case 1: An odd value from deck 1 that is not a multiple of 3 must be multiplied by a multiple of 6.
In deck 1, odd values that are not multiples of 3 are 11, 13, 17, and 19, yielding 4 options.
In deck 2, multiples of 6 are 12 and 18, yielding 2 options.
To combine these options, we multiply:
4*2 = 8.
Case 2: An even value from deck 1 that is not a multiple of 6 must be multiplied by a multiple of 3.
In deck 1, even values that are not multiples of 6 are 14, 16, and 20, yielding 3 options.
In deck 2, multiples of 3 are 12, 15 and 18, yielding 3 options.
To combine these options, we multiply:
3*3 = 9.
Case 3: An odd multiple of 3 from deck 1 must be multiplied by a multiple of 2.
In deck 1, the only odd multiple of 3 is 15, yielding 1 option.
In deck 2, even values are 12, 14, 16, 18 and 20, yielding 5 options.
To combine these options, we multiply:
1*5 = 5.
Case 4: A multiple of 6 from deck 1 can be multiplied by any value deck 2.
In deck 1, multiples of 6 are 12 and 18, yielding 2 options.
In deck 2, there are 10 values.
To combine these options, we multiply:
2*10 = 20.
(multiples of 6)/(total number of products) = (8+9+5+20)/(100) = 42/100 = .42.
The correct answer is
D.
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