From a deck of cards, one card is lost. What is the
probability that the lost card is either a 7 of clubs or 6 of
hearts?
Answers
Step-by-step explanation:
LetE
1
be the event that the lost card is a diamond. Given that there are 13 diamonds in the deck,P(E
2
)=
52
13
=
4
1
Let E
2
be the event that the lost card is not a diamond. P(E
2
)=1−
52
13
=
52
39
=
4
3
Let A be the event that the two cards drawn are found to be both diamonds.
We need to calculate P (2 cards are both diamond w the lost card being a diamond) next.
Given 13 diamond cards, if one is lost, then we have 12 remaining diamonds out of 51 total cards now.
The two cards that are both diamond can be drawn in
12
C
2
=
1×2
12×11
=
2
132
= 66 ways.
Likewise, the two diamonds can be drawn from the pack of 51 remaining cards in
51
C
2
=
1×2
51×50
=
2
2550
= 1275 ways.
Therefore, the P (2 cards drawn are diamond given one is lost) = P(A∣E
1
)
1275
66
Now, consider the event where the two cards drawn are both diamonds but the lost card is not a diamond.
The two cards that are both diamond can be drawn in
13
C
2
=
1×2
13×12
=
2
156
= 78ways.
Likewise, the two diamonds can be drawn from the pack of 51 remaining cards in
51
C
2
=
1×2
51×50
=
2
2550
= 1275 ways.
Therefore, the P (2 cards drwan are diamond given one card which is not a diamond is lost) = P(A∣E
1
)
1275
78
We need to calcuate the probability that the lost card is a diamond. P(E
1
∣A).
We can use Baye's theorem, according to which P(E
1
∣A)=
1275
66
.
4
1
+
1275
78
.
4
3
1275
66
.
4
1
=
66+78×3
66
=
300
66
=
50
11
P(E
1
∣A)=
1275
66
.
4
1
+
1275
78
.
4
3
1275
66
.
4
1
=
66+78×3
66
=
300
66
=
50
11
I hope it's helpful for u
plz. mark me as brainlest
follow me
1/26
Explanation:
The total number of cards in a deck = 52
The favorable outcome = 2
( 7 of clubs or 6 of hearts)
Therefore,
The probability of 7 of clubs or 6 of hearts is
= 1/52 + 1/52
= 2/52
The probability that the lost card is either a 7 of clubs or 6 of hearts is equal to 2/26.
#SPJ5
https://brainly.in/question/117708
https://brainly.in/question/18252471