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The LOTTO is a state lottery, to win you must choose five numbers from 1 to 39 (white balls). Then select one more number from 1 to 19 red ball. a) Calculate the number of possible combinations to win the Jackpot, five white balls and one red. b) Calculate the probability of obtaining the five white balls and missing the red one. (use seven decimal places) c) Calculate the probability of hitting 3 white balls and missing the red ball. (use seven decimal places) d) Calculate the probability of hitting 2 white balls and hitting the red ball. (use seven decimal places)

          The LOTTO is a state lottery, to win you must choose five numbers from 1 to 39 (white balls).  Then select one more number from 1 to 19 red ball.
 a) Calculate the number of possible combinations to win the Jackpot, five white balls and one red.
 b) Calculate the probability of obtaining the five white balls and missing the red one.  (use seven decimal places)
 c) Calculate the probability of hitting 3 white balls and missing the red ball.  (use seven decimal places)
 d) Calculate the probability of hitting 2 white balls and hitting the red ball.  (use seven decimal places)
        
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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The LOTTO is a state lottery, to win you must choose five numbers from 1 to 39 (white balls). Then select one more number from 1 to 19 red ball. a) Calculate the number of possible combinations to win the Jackpot, five white balls and one red. b) Calculate the probability of obtaining the five white balls and missing the red one. (use seven decimal places) c) Calculate the probability of hitting 3 white balls and missing the red ball. (use seven decimal places) d) Calculate the probability of hitting 2 white balls and hitting the red ball. (use seven decimal places)
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Transcript

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00:01 To calculate the number of possible combinations to win the jackpot, five white and one red ball, we can use a formula for combinations or use a calculator for combinations.
00:13 And so for part a, when you're looking for just how many possible combinations are there, well, that would be you want 39, you want to choose five from 39 white balls, and you want to choose one from 19 red balls.
00:44 And so you would want to calculate that.
00:50 Now, if you're on decimals, then you can just go to the functions and scroll all the way down to ncr.
00:58 If you're on a handheld calculator, you can do the same single map probability, and you'll find something like that looks like ncr here.
01:06 And so 39, choose five.
01:12 Times 19 choose one comes out to 10 ,939 ,000, 3 ,383 different possibilities.
01:52 For part b, to calculate the probability of obtaining the five white bottles and missing the red one, that would be, well, we need to divide the number of successful outcomes obtaining the five white bottles balls by the total number of possible outcomes, obtaining any combination of five white balls and one red ball.
02:21 So there's only one combination of five white balls that will not win the jackpot.
02:27 Since we're assuming that all of the balls are drawn randomly and independently, and the combination of five white balls has no effect on the red ball.
02:33 So the probability of obtaining the five white balls and missing the red one would be just one out of 39 choose five times.
02:56 Well, we were already calculated.
02:58 I guess i don't need to recalculate it.
03:04 This would just be how many different ways to pick that could win it.
03:19 And i would just leave it as a fraction because that's going to be a really small decimal.
03:34 But i think the spirit of this question is that probably to obtain the five white balls and missing the one red one really would just be one combination.
03:47 So i guess we will calculate it because it does say use seven decimals.
03:51 So let's do that.
03:57 1 divided by 10 ,939 ,383 would be .00009.
04:27 Oh, actually, i'm off because we would just round that up to 0 .01.
04:46 I was off anyways...
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