NIMCET 2025 Paper

Section: Mathematics

Question : 6 of 120

Marks: +1, -0

There are two coins, a blue and a red coin.
For the blue coin, the probability of getting a head is

0 . 9 9

, and for the red coin, it is

0 . 0 1

.
One coin is chosen randomly and is tossed.
The probability of getting a head is:

Solution:

There are two stages:
1. A coin is chosen at random.
So,

\;P(\;\text " blue coin "\;)=\;{1}/{2}

\;P(\;\text " red coin "\;)=\;{1}/{2}

2. The chosen coin is tossed.
We want

P(

Head

)

.
Use the law of total probability:

P(\;\text " Head "\;)=P(\;\text " Head "\; ∣ \;\text " blue "\;) ⋅ P(\;\text " blue "\;)+P(\;\text " Head "\; ∣ \;\text " red "\;) ⋅ P(\;\text " red "\;)

Substitute the values:

P(\;\text " Head "\;)=0.99 ⋅ \;{1}/{2}+0.01 ⋅ \;{1}/{2}

P(\;\text " Head "\;)=\;{0.99+0.01}/{2}=\;{1.00}/{2}=0.5

Answer:
0.5

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