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STD 11 - 14. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
Two persons each make a single throw with a die. The probability they get equal value is ${p_1}$. Four persons each make a single throw and probability of three being equal is ${p_2}$, then
  • A
    ${p_1} = {p_2}$
  • B
    ${p_1} < {p_2}$
  • ✓
    ${p_1} > {p_2}$
  • D
    None of these
✓

Answer

Correct option: C.
${p_1} > {p_2}$
c
(c) ${p_1} = \frac{6}{{36}} = \frac{1}{6}$

To find ${p_2},$ the total number of ways $ = {6^4}$and since two numbers out of $6$ can be selected in ${}^6{C_2}$ ways

$i.e.$ $15$ ways and corresponding to each of these ways, there are $8$ ways e.g., $(1,\,\,1,\,\,1,\,\,2)\,\,(1,\,\,1,\,\,2,\,\,1)\,.....$

Thus favourable ways $ = 15 \times 8 = 120$

Hence ${p_2} = \frac{{120}}{{{6^4}}} = \frac{5}{{54}}$. Hence ${p_1} > {p_2}.$

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