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16 May 2022, 08:03
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E
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Difficulty:
25%
(medium)
Question Stats:
73% (00:59) correct
27%
(00:52)
wrong
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There are 6 cards numbered from 1 to 6. They are placed into a box, and then one is drawn and put back and then another card is drawn and put back. What is the probability that the sum of the two cards will be 8?
A. \(\frac{2}{3}\)
B. \(\frac{1}{2}\)
C. \(\frac{5}{12}\)
D. \(\frac{2}{5}\)
E. \(\frac{5}{36}\)
A. \(\frac{2}{3}\)
B. \(\frac{1}{2}\)
C. \(\frac{5}{12}\)
D. \(\frac{2}{5}\)
E. \(\frac{5}{36}\)
16 May 2022, 08:03
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Official Solution:
There are 6 cards numbered from 1 to 6. They are placed into a box, and then one is drawn and put back and then another card is drawn and put back. What is the probability that the sum of the two cards will be 8?
A. \(\frac{2}{3}\)
B. \(\frac{1}{2}\)
C. \(\frac{5}{12}\)
D. \(\frac{2}{5}\)
E. \(\frac{5}{36}\)
\(P(sum \ of \ 8) = \)
\(=P(5, 3) + P(3, 5) + P(6, 2) + P(2, 6) + P(4, 4) = \)
\(=(\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) =\)
\(= \frac{5}{36}\).
Practice two other similar questions HERE and HERE.
Answer: E
There are 6 cards numbered from 1 to 6. They are placed into a box, and then one is drawn and put back and then another card is drawn and put back. What is the probability that the sum of the two cards will be 8?
A. \(\frac{2}{3}\)
B. \(\frac{1}{2}\)
C. \(\frac{5}{12}\)
D. \(\frac{2}{5}\)
E. \(\frac{5}{36}\)
\(P(sum \ of \ 8) = \)
\(=P(5, 3) + P(3, 5) + P(6, 2) + P(2, 6) + P(4, 4) = \)
\(=(\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) + (\frac{1}{6}*\frac{1}{6}) =\)
\(= \frac{5}{36}\).
Practice two other similar questions HERE and HERE.
Answer: E
15 Nov 2024, 07:15
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Total Outcomes= 6 X 6 = 36
Here order matters
2 cards are drawn with replacement
Sum should be 8, this is possible with (2,6), (3,5), (4,4), (5,3), (6,2)
Favourable outcomes = 5
Probability = 5/36
Here order matters
2 cards are drawn with replacement
Sum should be 8, this is possible with (2,6), (3,5), (4,4), (5,3), (6,2)
Favourable outcomes = 5
Probability = 5/36
