An urn contains 10 white and 5 red balls. If two balls are drawn at...

Total number of balls in the urn = $10 + 5 = 15$

Number of ways to draw $2$ balls from $15$ balls = $^{15}C_{2}$

Number of ways to draw $2$ red balls from $5$ red balls = $^{5}C_{2}$

Required probability = $\dfrac{^{5}C_{2}}{^{15}C_{2}}$

$^{5}C_{2} = \dfrac{5 \times 4}{2} = 10$

$^{15}C_{2} = \dfrac{15 \times 14}{2} = 105$

Required probability = $\dfrac{10}{105} = \dfrac{2}{21}$