Multiple choice

A die is thrown $400$ times, the frequency of the outcomes of the events are given as under. outcome $1$ $2$ $3$ $4$ $5$ $6$ Frequency $70$ $65$ $60$ $75$ $63$ $67$ Find the probability of occurrence of an odd number.

  1. The probability of occurrence of odd number$=\dfrac{5}{7}$
  2. The probability of occurrence of odd number$=\dfrac{9}{2}$
  3. The probability of occurrence of odd number$=\dfrac{193}{400}$
  4. The probability of occurrence of odd number$=\dfrac{200}{299}$
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C Correct answer
Explanation

Odd outcomes are 1, 3, and 5. Frequencies are 70, 60, and 63. Total odd frequency = 70 + 60 + 63 = 193. Total trials = 400. Probability = 193/400.

AI explanation

To find the empirical probability of an odd number, divide the total frequency of the odd outcomes by the total number of throws. The frequencies of the odd numbers 1, 3, and 5 are 70, 60, and 63 respectively, which sum to 193 favourable occurrences. The probability is 193 divided by the total frequency of 400, which equals 193/400.

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