Question

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

Answer 1

The probability is approximately 0.7427.

Explanation:

`"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

`189/256`

Explanation:

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