if 4 cards are drawn at random from a deck what is the probability that at least one is a heart?
in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

There is a probability of 1/4 that the first card drawn is a spade. That leaves 51 cards, including the 12 remaining spades. The chance that the second card drawn is not a spade is 39/51; then this goes to 39/50 for the third card; and for the fourth card it is 39/49. So the total probability we have: 1/4*39/51*39/50*39/49=0.118685 approx.

But we can also have the probability of not drawing a spade as the first card=3/4; the second card is a spade=13/51; the third card not a spade=39/50 (as before); the fourth card not a spade=39/49 (as before). But 1/4*39/51=3/4*13/51, so the probability of drawing just one spade within 4 cards is 4*0.118685=0.4747 or 47.47% approx., because any of the four cards can be the spade.

by Top Rated User (1.2m points)

Related questions

1 answer
asked Mar 10, 2013 in Statistics Answers by anonymous | 996 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,516 questions
100,279 answers
2,420 comments
732,215 users