Question

you have five red cards and six green cards. Draw seven times without replacement. let x be the number of red cards drawn. find the following:. P(X=4)

Answer 1

Total cards = 5 red + 6 green = 11 cards.

Draw seven times without replacement

let x be the number of red cards drawn

We have to find P( X = 4 )

i.e 4 red cards and 3 green cards in 7 cards.

Number of ways to select 4 red cards from 5 = 5C4 = 5

Number of ways to select 3 green cards from 6 = 6C3 = 20

So, number of ways to occurs 4 red and 3 green card = 5*20 = 100

Total number of ways to select 7 cards from 11 = 11C7 =330

So, probability that 4 red cards drawn is

P( X = 4 ) = 100/330 = 0.303