4 cards selected randomly from pack of 52 cards find the probability of selecting at most one heart card?

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Answer 1 · 2018-06-26T17:10:07

The probability is approximately 0.7427.

$"P"("at most 1 heart") = "P"("0 hearts") + "P"("1 heart")$

$"P"("0 hearts") = (""_39C_4)/(""_52C_4) = 82251/270725$

$"P"("1 heart") = (""_13C_1 xx ""_39C_3)/(""_52C_4)=(13 xx 9139)/270725=118807/270725$

$:.$
$"P"("at most 1 heart") = 82251/270725+118807/270725$

$color(white)("P"("at most 1 heart"))= 201058/270725$

$color(white)("P"("at most 1 heart"))= 15466/20825" "~~74.27%$

Answer 2 · 2018-06-26T17:21:47

$189/256$

We can set up a binomial distribution

$X tilde "" B(4,1/4)$

So at most hence meaning

$P(X<=1) = P(X=0) +P(X=1)$

For $X tilde "" B(n,p)$

$P(X=x) = (nCx)* p^x* (1-p)^(n-x)$

$P(X=0)+P(X=1) = ...$

$... = ((4C0 ) * 1/4 ^ 0 * 3^4/4^4) +( (4C1) * 1/4^1 + 3^3/4^3)$

$= 189/256$

NOTE : This solution is based upon replacing the card each time