Ritu has 3 shirts in shades of red , 4 in yellow shades and 5 in green shades…
2023
Ritu has 3 shirts in shades of red , 4 in yellow shades and 5 in green shades .Three shirts are picked at random. The probability that all of those are in red shades is:
- A.
1/12
- B.
1/660
- C.
1/66
- D.
1/4
Attempted by 13 students.
Show answer & explanation
Correct answer: B
Solution:
Total shirts: 3 + 4 + 5 = 12; red shirts = 3.
Method 1 (sequential probability):
Probability first shirt is red = 3/12.
Probability second shirt is red (after one red removed) = 2/11.
Probability third shirt is red (after two red removed) = 1/10.
Multiply these probabilities: (3/12) * (2/11) * (1/10) = 6/1320 = 1/220.
Method 2 (combinatorial):
Number of ways to choose 3 red shirts = C(3,3) = 1.
Total ways to choose any 3 shirts = C(12,3) = 220.
So probability = 1/220.
Answer: The correct probability that all three selected shirts are red is 1/220.
Note: The provided answer key listing 1/660 is incorrect. The correct value is 1/220 as shown above.