JEE Main 2025 Jan 23 Shift 1, Mathematics Q20: Introduction To Probability

JEE Main2025Jan 23, Shift 1Mathematics

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
$\frac{1}{2}$
B
$\frac{3}{5}$
C
$\frac{2}{3}$
D
$\frac{4}{9}$

Solution

Die 1 face probabilities (out of 6): $P (1) = 2/6$ , $P (2) = 2/6$ , $P (3) = 1/6$ , $P (4) = 1/6$ .

Die 2 face probabilities: $P (1) = 1/6$ , $P (2) = 2/6$ , $P (3) = 2/6$ , $P (4) = 1/6$ .

Outcomes giving sum 4 or 5: $(1, 3), (2, 2), (3, 1), (1, 4), (2, 3), (3, 2), (4, 1)$ . Compute each probability $P (a) \cdot Q (b)$ :

$(1, 3) : \frac{2}{6} \cdot \frac{2}{6} = \frac{4}{36}$

$(2, 2) : \frac{2}{6} \cdot \frac{2}{6} = \frac{4}{36}$

$(3, 1) : \frac{1}{6} \cdot \frac{1}{6} = \frac{1}{36}$

$(1, 4) : \frac{2}{6} \cdot \frac{1}{6} = \frac{2}{36}$

$(2, 3) : \frac{2}{6} \cdot \frac{2}{6} = \frac{4}{36}$

$(3, 2) : \frac{1}{6} \cdot \frac{2}{6} = \frac{2}{36}$

$(4, 1) : \frac{1}{6} \cdot \frac{1}{6} = \frac{1}{36}$

Total $= \frac{4 + 4 + 1 + 2 + 4 + 2 + 1}{36} = \frac{18}{36} = \frac{1}{2}$ .

Concept behind this question

Introduction To ProbabilityNotes, formulas and examples →

Practice more Mathematics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2025 Jan 23 Shift 1, Mathematics Q20: Introduction To Probability

Concept behind this question

More previous year questions on Introduction To Probability

Practice more Mathematics