SOLUTION: ten cards are numbered 1 through 10. three cards are selected. find the probability that all three cards are less than 5.

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Question 701774: ten cards are numbered 1 through 10. three cards are selected. find the probability that all three cards are less than 5.
Found 2 solutions by vheroli, jsmallt9:
Answer by vheroli(126) About Me  (Show Source):
You can put this solution on YOUR website!
Cards that are less than 5 are 1,2,3,and 4:
P(C)= 4/10 = 2/5

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I think the other tutor did not notice that three cards are to be drawn. His/her solution is only correct for drawing a single card.

To find the probability of all three cards being less than 5:
  1. Find the individual probabilities of each card being less than 5; then
  2. Multiply these probabilities.
The probability of the first card being less than 5 is, as the other tutor said, 4/10.

The probability of the second card being less than 5 is 3/9 since there are only three cards left that are less than 4 and there are only 9 cards altogether after the first card.

The probability of the third card being less than 5 is 2/8 since there are only two cards left that are less than 4 and there are only 8 cards altogether after the first two cards.

The probability of all three cards being less than 5 is the product of the three individual probabilities:
%284%2F10%29%2A%283%2F9%29%2A%282%2F8%29
which simplifies down to:
1%2F30