Find the probablity a card drawn from awell shu
Answers
Answer:
In a deck of 52 cards, there are 13 spades.
Let X be the random variable denoting the number of success and success here is getting a spade for an event when two cards are drawn simultaneously.
∴We can say that the number of successes is equal to some spades obtained in each draw.
∴X can take values 0,1 or 2.
P(X=0)=
52
C
2
39
C
2
=
52×51
39×38
=
34
19
[For selecting 0 spades, we removed all 13 spades from the deck and selected out of 39]
P(X=1)=
52
C
2
13
C
1
×
39
C
1
=
52×51
13×39×2
=
34
13
[For selecting 1 spade, we need to select and 1 out of 13 spade and not any other spade]
P(X=2)=
52
C
2
13
C
2
=
52×51
13×12
=
34
2
[For selecting 2 spades, we need to select and 2 out of 13 spades]
Now we have p
i
and x
i
.
∴The probability distribution for X is
P(X=0)=
34
19
,P(X=1)=
34
13
,P(X=2)=
34
2