JEE 2025 Mathematics PYQ — Two balls are selected at random one by one without replacement f… | Mathem Solvex | Mathem Solvex
Tip:A–D to answerE for explanationV for videoS to reveal answer
JEE 2025 — Mathematics PYQ
JEE | Mathematics | 2025
Two balls are selected at random one by one without replacement from a bag containing four white and six black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is , </span></strong><strong><spanstyle="font−size:14pt;">m/</span></strong><strong><spanstyle="font−size:14pt;">nwhere gcd(m,n)=1, then </span></strong><strong><spanstyle="font−size:14pt;">m+n is equal to:
Choose the correct answer:
A.
14
(Correct Answer)
B.
4
C.
11
D.
13
Correct Answer:
14
Explanation
E1= First selected ball is white. E2= First selected ball is black. A= Second selected ball is black. P(E2/A)=P(E1)⋅P(A/E1)+P(E2)P(A/E2)P(E2)⋅P(A/E2)=106×95+106×95104×95=24+3030=5430=95∴m+n=5+9=14.
Explanation
E1= First selected ball is white. E2= First selected ball is black. A= Second selected ball is black. P(E2/A)=P(E1)⋅P(A/E1)+P(E2)P(A/E2)P(E2)⋅P(A/E2)=106×95+106×95104×95=24+3030=5430=95∴m+n=5+9=14.
