1 in 4 wins

Probability Level pending

MickeyD has a lottery scratch card that claims "1 in 4 wins". Assuming that there are many scratch cards so that the chance that each card wins is 1/4 independently.

What is the approximate probability that when you scratch 4 lottery cards, you will win a prize?

70% 80% 90% 100%

Chung Kevin by Chung Kevin , 46, Australia

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1 solution

Zee Ell
Oct 30, 2016

The probability of not winning a prize, when scratching 4 cards:

( 1 − 0.25 ) 4 = 0.7 5 4 = 0.31640625 (1-0.25)^4 = 0.75^4 = 0.31640625

Hence, the probability of winning at least one prize, when scratching 4 cards:

1 − ( 1 − 0.25 ) 4 = 1 − 0.7 5 4 = 1 − 0.31640625 = 1- (1-0.25)^4 = 1- 0.75^4 = 1 - 0.31640625 =

= 0.68359375 = 70 % ( 1 s. f. ) = 0.68359375 = \boxed { 70 \% } \text { ( 1 s. f. ) }

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Does this percentage feel low to you? I thought it would be much closer to 100%.

Chung Kevin - 4 years, 7 months ago

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It felt low when I first solved a similar problem a couple of years ago. After thinking about it, I realised that it should be correct. (This percentage also includes multiple wins.)

Zee Ell - 4 years, 7 months ago

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