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Five tiles which are marked individually with the letters A to E are placed into a bag, and randomly drawn out one by one without being replaced. What is the probability that the tile with the letter B is pulled out immediately after the tile with the letter A?
A. 1/5
B. 2/5
C. 1/10
D. 1/30
E. 1/120
A. 1/5
B. 2/5
C. 1/10
D. 1/30
E. 1/120
Question -
I solved it as, group "AB" as one, and the other 4 letters individually. So, now we have 4! waves of desired outcomes. Total number of outcomes in 5!. Answer is 1/5. Is my logic correct?
Answer is 1/5 (A)
I solved it as, group "AB" as one, and the other 4 letters individually. So, now we have 4! waves of desired outcomes. Total number of outcomes in 5!. Answer is 1/5. Is my logic correct?
Answer is 1/5 (A)
25 Aug 2022, 04:52
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Kaur92
So, there are 5 letters in the bag: A, B, C, D, and E. We are interested in the following outcomes:
ABXXX: 1/5*1/4 = 1/20;
XABXX: 3/5*1/4*1/3 = 1/20;
XXABX: 3/5*2/4*1/3*1/2 = 1/20;
XXXAB: 3/5*2/4*1/3*1/2*1 = 1/20;
The sum of the above is 1/20 + 1/20 + 1/20 + 1/20 = 4/20 = 1/5.
Answer: A.
OR: P = Favorable/Total
Number of favorable outcomes: consider A and B as one unit: {AB}. Four units {AB}, {C}, {D}, and {E} can be arranged in 4! ways. In all of these outcomes B will be immediately after A:
- {AB}{C}{D}{E};
{AB}{C}{E}{D};
{AB}{D}{C}{E};
{AB}{D}{E}{C};
{AB}{E}{C}{D};
{AB}{E}{D}{C};
...
{C}{E}{D}{AB};
Total number of outcomes: five letters A, B, C, D, and E can be arranged in 5! ways.
P = Favorable/Total = 4!/5! = 1/5.
Answer: A.
General Discussion
25 Aug 2022, 05:12
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Given: Five tiles which are marked individually with the letters A to E are placed into a bag, and randomly drawn out one by one without being replaced.
Asked: What is the probability that the tile with the letter B is pulled out immediately after the tile with the letter A?
Total ways = 5!
Favorable ways = 4! after considering AB as one single letter
Probability that the tile with the letter B is pulled out immediately after the tile with the letter A = 4!/5! = 1/5
IMO A
Asked: What is the probability that the tile with the letter B is pulled out immediately after the tile with the letter A?
Total ways = 5!
Favorable ways = 4! after considering AB as one single letter
Probability that the tile with the letter B is pulled out immediately after the tile with the letter A = 4!/5! = 1/5
IMO A
