Multiple choice

A coin is tossed twice. Events E and F are defined as follows :E=heads on first toss, F= heads on second toss.Find the probability of $\displaystyle E\cup F.$

  1. Hence p $\displaystyle(E\cup F) =\frac{1}{4}$
  2. Hence p $\displaystyle(E\cup F) =\frac{3}{4}$
  3. Hence p $\displaystyle(E\cup F) =\frac{1}{2}$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P(E) = 1/2, P(F) = 1/2. Since events are independent, P(E intersect F) = 1/4. P(E union F) = P(E) + P(F) - P(E intersect F) = 1/2 + 1/2 - 1/4 = 3/4.

AI explanation

We use the addition theorem of probability, which states that the probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection. The probability of getting a head on the first toss is 1/2, the probability of getting a head on the second toss is 1/2, and the probability of getting heads on both tosses is 1/4. Therefore, the probability of the union is 1/2 plus 1/2 minus 1/4, which equals 3/4.

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