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MHT CET202313 May 2023Evening ShiftMathematicsProbabilityActual

A random variable X has the probability distribution array |l|c|c|c|c|c|c|c|c| X =x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 P ( X =x) & 0.15 & 0.23 & 0.12 & 0.20 & 0.08 & 0.10 & 0.05 & 0.07 array For the events E = X is a prime number and F = x < 5 , P ( E F ) is

Options

  1. A0.63
  2. B0.75
  3. C0.83
  4. D0.90

Correct answer

C. 0.83

Step-by-step solution

aligned P ( E )= & P ( X =2 or X =3 or X =5 or X =7) = & P ( X =2)+ P ( X =3)+ P ( X =5) & + P ( X =7) aligned aligned & =0.15+0.23+0.12+0.20 & =0.7 aligned aligned P ( E F ) & = P ( X is a prime number less than 5) & = P ( X =2)+ P ( X =3) & =0.23+0.12 & =0.35 P ( E F ) & = P ( E )+ P ( F )- P ( E F ) & =0.48+0.7-0.35 & =0.83 aligned

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