JAMIA 2023 — Mathematics PYQ

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Question

JAMIA 2023 — Mathematics PYQ

JAMIA | Mathematics | 2023

A card is drawn from a pack of 52 cards. A gambler bets that it is a spade or an ace. What are odds against his winning this bet?

Choose the correct answer:

Explanation

Solution:

Ek pack mein total cards ki sankhya:

n(S) = 52

Maan lijiye $E$ woh event hai jisme card 'spade' ya 'ace' nikalta hai.

Taash ki gaddi mein total Spades ki sankhya: $13$
Taash ki gaddi mein total Aces ki sankhya: $4$
'Ace of Spades' ek aisa card hai jo dono mein common hai, isliye ise ek baar ghatana hoga.

Favorable outcomes ki sankhya $n(E)$ :

n(E) = n(\text{Spades}) + n(\text{Aces}) - n(\text{Spade and Ace})

n(E) = 13 + 4 - 1

n(E) = 16

Winning ke against outcomes (Losing outcomes) ki sankhya:

n(E^c) = n(S) - n(E)

n(E^c) = 52 - 16

n(E^c) = 36

Odds against winning ka formula hota hai:

\text{Odds against} = \frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}

\text{Odds against} = \frac{36}{16}

Isse simplify karne par:

\text{Odds against} = \frac{9}{4}

Yani, odds against his winning $9:4$ hain.

Choose the correct answer:

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