MAH-CET 2025 — Mathematics PYQ

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Question

MAH-CET 2025 — Mathematics PYQ

MAH-CET | Mathematics | 2025

A game consists of tossing a one-rupee coin 3 times and noting its outcome each time. Tanmay wins if all the tosses give the same result, i.e. three heads or three tails, and loses otherwise. Calculate the probability that Tanmay will lose the game.

Choose the correct answer:

Explanation

Solution

1. Total Outcomes

Jab ek coin 3 baar toss kiya jata hai, toh total outcomes (S) ye hote hain:

$S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$

Iska matlab, total outcomes ki sankhya hai:

$n(S) = 8$

2. Winning Outcomes

Tanmay tab jeet-ta hai jab teeno tosses ka result same ho (yaani teeno Heads ya teeno Tails).

Winning outcomes $(W) = \{HHH, TTT\}$

$n(W) = 2$

3. Losing Outcomes

Tanmay tab haarega jab outcome "same result" na ho. Iska matlab total outcomes mein se winning outcomes ko ghata (subtract) dena hai:

Losing outcomes $(L) = 8 - 2 = 6$

Wo outcomes hain: $\{HHT, HTH, THH, HTT, THT, TTH\}$

$n(L) = 6$

4. Probability of Losing

Probability ka formula hota hai:

P(\text{Losing}) = \frac{\text{Number of favorable outcomes (Losing)}}{\text{Total number of outcomes}}

Values put karne par:

P(\text{Losing}) = \frac{6}{8}

Isse simplify karne par:

P(\text{Losing}) = \frac{3}{4}