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Probability question

2003 · Shift 0 · Q76
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Probability question

2003 · Shift 0 · Q76

JEE MainMathematicsProbabilityMCQ+4 / −1
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is :
  1. A
    25{{2 \over 5}}52​
  2. B
    45{{4 \over 5}}54​
  3. C
    35{{3 \over 5}}53​
  4. D
    15{{1 \over 5}}51​
View written solutionFree

Correct answer: A

  1. Understand the experiment

There are 555 horses in the race, and exactly one horse will win.

Mr. A selects 222 horses at random and bets on them. We need the probability that the winning horse is among the 2 selected horses.

  1. Method 1: Direct probability

Out of the 555 horses, Mr. A has chosen 222.

Since each horse is equally likely to be the winner, the probability that the winner is one of these 222 chosen horses is

25.\frac{2}{5}.52​.
  1. Method 2: Using combinations (verification)

Total number of ways to choose 222 horses out of 555:

(52)=10.\binom{5}{2} = 10.(25​)=10.

Now count favorable selections: for Mr. A to include the winning horse, he must choose the winning horse and 111 more horse from the remaining 444 horses.

Thus favorable ways are

(41)=4.\binom{4}{1} = 4.(14​)=4.

So the probability is

410=25.\frac{4}{10} = \frac{2}{5}.104​=52​.
  1. Evaluate the options
  • A: 25\frac{2}{5}52​ ✅
  • B: 45\frac{4}{5}54​ ❌
  • C: 35\frac{3}{5}53​ ❌
  • D: 15\frac{1}{5}51​ ❌

Therefore, the correct option is A.

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