JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Probability

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One die has two faces marked 1 , two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

(A) $\frac{1}{2}$ ✓ Correct
(B) $\frac{3}{5}$
(C) $\frac{2}{3}$
(D) $\frac{4}{9}$

Answer: (A)

Solution

Die 1:

P (1) = P (2) = \frac{2}{6}

P (3) = P (4) = \frac{1}{6}

.
Die 2:

P (1) = P (4) = \frac{1}{6}

P (2) = P (3) = \frac{2}{6}

.

Sum

= 4

: outcomes

(1, 3), (2, 2), (3, 1)

P (sum = 4) = \frac{2}{6} \cdot \frac{2}{6} + \frac{2}{6} \cdot \frac{2}{6} + \frac{1}{6} \cdot \frac{1}{6} = \frac{4 + 4 + 1}{36} = \frac{9}{36}

Sum

= 5

: outcomes

(1, 4), (2, 3), (3, 2), (4, 1)

P (sum = 5) = \frac{2}{6} \cdot \frac{1}{6} + \frac{2}{6} \cdot \frac{2}{6} + \frac{1}{6} \cdot \frac{2}{6} + \frac{1}{6} \cdot \frac{1}{6} = \frac{2 + 4 + 2 + 1}{36} = \frac{9}{36}

P (sum = 4 or 5) = \frac{9}{36} + \frac{9}{36} = \frac{18}{36} = \frac{1}{2}

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Probability

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