Test Index

NDA Math Probability

Question : 68 of 100

Marks: +1, -0

Solution:

Let X denote the no. of coins showing 3 or more heads in a set of 7 coins

X follows binomial distribution with

n=7

p = probability of getting a head in a single toss of a coin

\Rightarrow p=\frac{1}{2}

; thus

q=1-p=\frac{1}{2}

∴ Probability of getting at least 3 heads

=P(x\geq 3)

=1-P(x<3)

=1-\left[P(x=0)+P(x=1)+P(x=2)\right]

=1-\left[{}^{7}C_{0}+{}^{7}C_{1}+{}^{7}C_{2}\right]\;\;\frac{1}{2^{7}}

=\;\;\frac{128}{128}-\;\;\frac{29}{128}=\;\;\frac{99}{128}

∴ No. of throws

=\;\;\frac{99}{128}\times 128=99

Go to Question:

Prev Question

Next Question