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) (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) (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:- Find the individual probabilities of each card being less than 5; then
- 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:
which simplifies down to:
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