Multiple choice

If three coins are tossed, represent the sample space and the event of getting at least two heads also find the number of elements in them.

  1. $n(S)=8$ and $n(E)=4$
  2. $n(S)=8$ and $n(E)=1$
  3. $n(S)=8$ and $n(E)=7$
  4. $n(S)=8$ and $n(E)=3$
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A Correct answer
Explanation

For three coins, the sample space S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}, so n(S)=8. The event E of getting at least two heads is {HHH, HHT, HTH, THH}, so n(E)=4.

AI explanation

When three coins are tossed, the total number of elements in the sample space is found using the multiplication principle of counting as 2 * 2 * 2 = 8, meaning n(S)=8. The event of getting at least two heads includes the outcomes with exactly two heads and the outcome with three heads. Counting the combinations for exactly two heads gives 3 outcomes, and adding the 1 outcome for three heads means n(E)=4.

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