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NIMCET 2025 Paper

Section: Mathematics

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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

0.99

, and for the red coin, it is

0.01

One coin is chosen randomly and is tossed.

The probability of getting a head is:

0.98
1
0.02
0.5

Solution:

There are two stages:

1. A coin is chosen at random.

So,

P(\text{blue coin}) = \frac{1}{2}

P(\text{red coin}) = \frac{1}{2}

2. The chosen coin is tossed.

We want

P(

Head

)

.

Use the law of total probability:

P(\text{Head}) = P(\text{Head} \mid \text{blue}) \cdot P(\text{blue}) + P(\text{Head} \mid \text{red}) \cdot P(\text{red})

Substitute the values:

P(\text{Head}) = 0.99 \cdot \frac{1}{2} + 0.01 \cdot \frac{1}{2}

P(\text{Head}) = \frac{0.99+0.01}{2} = \frac{1.00}{2} = 0.5

Answer:

0.5

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