Multiple choice

$(A)$A die is thrown once. Find the probability of getting $(i)$ a multiple of $2$ $(ii)$ A number lying between $1$ and $5$ $(iii)$ A child has a die whose six faces show the letters as shown below A B C D E A $(B)$The die is thrown once. What is the probability of getting $(i) A,: (ii) D$?

  1. $(A)\space (i)\space \displaystyle\frac{1}{3}\quad (ii) \space \displaystyle\frac{1}{2}\quad (iii)\space \displaystyle\frac{1}{5} \\ (B)\space (i)\space \displaystyle\frac{1}{2}\quad (ii) \displaystyle\frac{1}{6}$
  2. $(A)\space (i)\space \displaystyle\frac{1}{3}\quad (ii) \space \displaystyle\frac{1}{2}\quad (iii)\space \displaystyle\frac{1}{2} \\ (B)\space (i)\space \displaystyle\frac{1}{2}\quad (ii) \displaystyle\frac{1}{3}$
  3. $(A)\space (i)\space \displaystyle\frac{1}{2}\quad (ii) \space \displaystyle\frac{1}{2}\quad (iii)\space \displaystyle\frac{1}{2} \\ (B)\space (i)\space \displaystyle\frac{1}{3}\quad (ii) \displaystyle\frac{1}{6}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A: (i) Multiples of 2 in {1,2,3,4,5,6} are {2,4,6}, prob = 3/6 = 1/2. (ii) Between 1 and 5 are {2,3,4}, prob = 3/6 = 1/2. (iii) Letters A,B,C,D,E,A. Prob(A) = 2/6 = 1/3. B: (i) Prob(A) = 2/6 = 1/3. (ii) Prob(D) = 1/6.

AI explanation

For part A, the multiples of 2 on a die are 2, 4, and 6, giving a probability of 3 divided by 6, or 1 divided by 2. The numbers lying strictly between 1 and 5 are 2, 3, and 4, which also gives a probability of 1 divided by 2. For part B, the die has six faces (A, B, C, D, E, A), so the probability of drawing A is 2 divided by 6, which is 1 divided by 3, and the probability of drawing D is 1 divided by 6. This matches the set of results where A(i) is 1/2, A(ii) is 1/2, B(i) is 1/3, and B(ii) is 1/6.

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