If three cards are drawn at random from a well-
shuffled pack of cards, then what is the probability
that each card is from a different suit?
Answers
Answer:
Step-by-step explanation:
Three Cards are drawn from a pack of 52 cards.
Let X be the number of red cards drawn.
In pack of 52 cards there are 26 red cards and 26 black cards.
We can draw 3 cards out of 52 in
52
C
3
ways.
P(X=0)=P( No red cards drawn )=
52
C
3
26
C
0
×
26
C
3
=
52×51×50
26×25×24
=
17
2
P(X=1)=P(One red cared drawn )=
52
C
3
26
C
1
×
26
C
2
=
3×2×1
52×51×50
26×
2×1
26×25
=
34
13
P(X=2)=P(Two red card drawn )=
52
C
3
26
C
2
×
26
C
1
=
3×2×1
52×51×50
2×1
26×25
×
1
26
=
34
13
P(X=3)=P( Three red card drawn )=
52
C
3
26
C
3
×
26
C
0
=
52×51×50
26×25×24
=
17
2
x
i
P(x
i
) x.P(x
i
)
0
17
2
0
1
34
13
34
13
2
34
13
34
26
3
17
2
17
6
∑x
i
.P(x
i
)=
2
3
⇒ Mean of the distribution =∑x
i
P(x
i
)=
2
3
=1.5