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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
MCQ
If three numbers are drawn at random successively without replacement from a set $S=\{1,2, \ldots, 10\}$, then the probability that the minimum of the chosen numbers is 3 or their maximum is 7 is
  • A
    $\frac{1}{40}$
  • B
    $\frac{3}{40}$
  • C
    $\frac{5}{40}$
  • ✓
    $\frac{11}{40}$
✓

Answer

Correct option: D.
$\frac{11}{40}$
(D)
$n ( S )={ }^{10} C _3$
A: event that minimum of chosen numbers is 3
B: event that maximum of chosen number is 7 .
$P ( A )=\frac{{ }^7 C _2}{{ }^{10} C _3}, P ( B )=\frac{{ }^6 C _2}{{ }^{10} C _3}, P ( A \cap B )=\frac{{ }^3 C _1}{{ }^{10} C _3}$
$=\frac{{ }^7 C _2}{{ }^{10} C _3}+\frac{{ }^6 C _2}{{ }^{10} C _3}-\frac{{ }^3 C _1}{{ }^{10} C _3}$
$=\frac{11}{40}$

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