Question

Jack randomly draws three cards from a normal deck of 52cards.What is the probability that the first card is a heart, the secondcard is a diamond, and the third card is not a spade if you donot replace the first card and the second? Enter your answer asa decimal rounded to the nearest thousandth.-

Answer 1

Three cards:

First card is a heart. There are 13 hearts in a normal deck:

`P=(13)/(52)=(1)/(4)`

Second card is a diamond: there are 13 diamonds:

`P_2=(13)/(52)=(1)/(4)`

Third: The card in not a spade, WITHOUT replacement.

There are 13*3 card that are not spade:

`P_3=(13*3)/(52)=(3)/(4)`

The probability will be given by:

`PTotal=P\cap P_2\cap P_3`

Replacing:

`PTotal=(1)/(4)*(1)/(4)*(3)/(4)=(3)/(64)=0.0468\approx0.047`

The answer is: 0.047.