Ronaldo L. I need help with the problem and how to get the answer
2 Answers By Expert Tutors
Danielle M. answered • 04/18/16
Patient Teacher/Instructional Designer for Math and Science Tutoring
Kenneth's answer looks right to me. In case you wanted more explanation of how to solve this, the problem is asking you to find the probability of one thing or another happening. You are asked to find the probability of either drawing a 5 or a heart. As Kenneth points out, there are 13 hearts (Ace, King, Queen, Jack, and numbers 2 through 10). So if you were just asked to find the probability of drawing a heart, it would be 13/52. But the problem also wants you to include (add) the probability of drawing a 5. There are four 5s in a deck, but you already included the 5 of hearts in 13/52. So you need to include the 3 other 5s (spades, clubs and diamonds). Adding up the probability of getting hearts OR 5s, you have 13/52 + 3/52 = 16/52.
You can reduce this fraction to 4/13. So that is your probability of drawing a heart or a 5.
Whenever you do probability problems, check to see if you are being asked to find probability of one thing OR another, or of multiple events happening together. For instance, if this problem asked you to find the probability of drawing a heart AND a 5, well, there is only one 5 of hearts in a deck. So that would be 1/52.
Hopefully this (long) explanation helped!
Kenneth S. answered • 04/18/16
Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
With 13 hearts in the deck, and three other cards (5s of spades, clubs and diamonds) in the definition of the Event,
From the standard 52-card deck, 5 cards are drawn randomly and is not put back. What is the probability that none of the ranks are the same? An example is 3, 5, 6, J, K.
I have tried this method, taking the product of each draw, but don't know if it's a valid method:
1st draw : $\frac{52}{52}$
2nd draw : 1 - $\frac{3}{51}$ = $\frac{48}{51}$ (Because there now is 51 cards left and three are bad.)
3rd draw : 1 - $\frac{6}{50}$ = $\frac{44}{50}$
4th draw : 1 - $\frac{9}{49}$ = $\frac{40}{49}$
5th draw : 1 - $\frac{12}{48}$ = $\frac{36}{48}$
P(x) = $\frac{52 * 48 * 44 * 40 * 36}{52 * 51 * 50 * 49 * 48}$ = $\frac{2112}{4165}$ ~= 50,7 %.
To me this seems like a weird and wrong answer, and I don't know how I would solve this problem generally.
Could someone please explain? :) Got exams in 12 hours, and got a feeling I need to know this :P
odds and probability are different, but related. odds for equals probability for divided by probability against. odds against equals probability against divided by probability for. there are 4 number 5's in the deck. they are the 5 of clubs, the 5 of spades, the 5 of hearts, and the 5 of diamonds. the probability of drawing a 5 from the deck is 4/52. the probability of not drawing a 5 from the deck is 48/52 the odds of drawing a 5 from the deck are 4/52 divided by 48/52 which is equal to 4/52 * 52/48 which is equal to 4/48 which is equal to 1/12 which means 1 to 12. the odds against drawing a 5 from the deck are 48/52 divided by 4/52 which is equal to 48/51 * 52/4 which is equal to 48/4 which is equal to 12/1 which means 12 to 1. your odds of drawing a five from the deck are 1 to 12. your odds against drawing a five from the deck are 12 to 1. when you roll a die, the probability of getting any number is 1/6. the probability of rolling a number greater than 3 equals the probability of rolling a 4 or a 5 or a 6 which is equal to 3/6 which is equal to 1/2. the probability of not rolling a number greater than 3 is also equal to 1/2. the odds of rolling a number greater than 3 is equal to 1/2 divided by 1/2 which is equal to 1/2 * 2/1 which is equal to 1/1 which means 1 to 1. the odds of not rolling a number greater than 3 is equal to 1/2 divided by 1/2 which is equal to 1/2 * 2/1 which is equal to 1/1 which means 1 to 1. the odds are considered even because the odds for is the same as the odds against. you convert odds to probability by adding the numerator and denominator together and that becomes the denominator of the probability. example: 4/5 odds becomes 4/9 probability. the 4 is added to the 5 and that gets you 9 which is the denominator of the probability. you convert probability to odds by subtracting the numerator from the denominator and that becomes the denominator of the odds. example: 4/9 probability becomes 4/5 odds. the 4 is subtracted from the 9 and that gets you 5 which is the denominator of the odds. here's a reference:
//www.mathplanet.com/education/pre-algebra/probability-and-statistic/finding-the-odds
note that odds for is equal to the number of chances to succeed divided by the number of chances to fail means the same as the probability of success divided by the probability of failure. example: you try 10 times. you get 2 successes out of 10 tries. the probability of success = 2/10 the probability of failure = 8/10 the odds of success = probability of success divided by probability of failure. this is equal to (2/10) / (8/10) which is equal to (2/10) * (10/8) which is equal to (2/8). the denominator of the probability cancels out in the division and you are left with 2/8. 2/8 is the number of successes divided by the number of failures. odds of success = probability of success / probability of failure = number of successes / number of failures.