India and Pakistan play a 5 match test series of hockey, the probability that India wins at least three matches is :

Question

India and Pakistan play a 5 match test series of hockey, the probability that India wins at least three matches is : (A) (1/2) (B) (3/5) (C) (4/5) (D) None of these

Tardigrade Admin · Accepted Answer

India win atleast three matches = 5C3 ((1/2))5 + 5C4 ((1/2))5 + 5C5 ((1/2))5 = ((1/2))5 (16) = (1/32) ×16 = (1/2)

Q. India and Pakistan play a 5 match test series of hockey, the probability that India wins at least three matches is :

$\frac{1}{2}$

$\frac{3}{5}$

$\frac{4}{5}$

None of these

India win atleast three matches
$=^{5} C_{3} (\frac{1}{2})^{5} +^{5} C_{4} (\frac{1}{2})^{5} +^{5} C_{5} (\frac{1}{2})^{5}$
$= (\frac{1}{2})^{5} (16) = \frac{1}{32} \times 16 = \frac{1}{2}$