Question

In a standard 52 card deck of playing cards, each card has one of four suits: spades, heart, club, or diamond. There are 13 cards of each suit. Alison thoroughly shuffles a standard deck, draws a card, then returns it to the deck, and shuffles again. She repeats this process until she has drawn 9 cards. Find the probability that she draws at most 3 spade cards, Use Excel to find the probability.

Answer 1

I will write the R Code for the above problem because it is more convenient than excel and easier too.

Here, in the 9 cards,we have to find that it contains at most 3 spades.

Here,let X denote no.of spades in the 9 cards.

Also,let p= P(getting a spade) =13/52 =0.25

Therefore,here X~ binomial (9,0.25)

We have to find P( at most 3 spades ) =P(X<=3)

R Code :

> pbinom(3,9,0.25)
[1] 0.8342743

You can cross check with the help of Binomial Probabilty Calculators available online.