Multiple choice

A coin is tossed and a die is thrown simultaneously : $P$ is the event of getting head and a odd number. $Q$ is the event of getting either $H$ or $T$ and an even number. $R$ is the event of getting a number on die greater than $7$ and a tail. $S$ is the sample space. Which of the following options is correct?

  1. $n(S) = 12, n(P) = 3, n(Q) = 2, n(R) = 0$
  2. $n(S) = 12, n(P) = 3, n(Q) = 3, n(R) = 0$
  3. $n(S) = 12, n(P) = 3, n(Q) = 6, n(R) = 0$
  4. $n(S) = 12, n(P) = 3, n(Q) = 5, n(R) = 0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sample space S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, n(S)=12. P (Head and odd) = {H1, H3, H5}, n(P)=3. Q (H or T and even) = {H2, H4, H6, T2, T4, T6}, n(Q)=6. R (Number > 7 and Tail) = {}, n(R)=0.

AI explanation

The sample space S for tossing a coin and throwing a die simultaneously contains 2 times 6, or 12, outcomes. Event P requires a head and one of the three odd die faces (1, 3, 5), so n(P) equals 3. Event Q requires an even die face (2, 4, or 6) and allows either coin face, giving 3 times 2, or 6, outcomes. A standard die has no face greater than 7, making n(R) equal to 0. This confirms n(S) = 12, n(P) = 3, n(Q) = 6, n(R) = 0.

Keep practicing — related questions