Question

You have ten different cards: the Ace through 5 of spades and clubs. Three cards are...

You have ten different cards: the Ace through 5 of spades and clubs. Three cards are selected at random without replacement. What is the probability of the sum of the numbers on the

three cards is divisible by 7 (use 1 fore Ace)

Math   Statistics-And-Probability   
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Answer #1

For divisibility by seven the sum of three cards should either be 7 or 14 (highest sum possible = 15)

Sum = 7

1 ace of spades, 1 ace of clubs, 5 of spades or 5 of clubs

probability = 1/10 * 1/9 * 2/8 = 2/720

2 of spades, 2 of clubs, 3 of spades or 3 of clubs

Probability = 2/720

1 of spades or 1 of clubs, 2 of spades or 2 of clubs, 4 of spades or 4 of clubs

probability = 2/10 x 2/9 x 2/8 = 8/720

3 of spades, 3 of clubs, 1 of spades or 1 of clubs

probability = 2/720

total probability of sum 7 = 14/720

Sum = 14

5 of spades, 5 of clubs, 4 of spades or 4 of clubs

probability = 2/720

So, probability sum is divisible by 7 = 14/720 + 2/720 = 16/720 = 1/45

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