Question

1. A fair coin is tossed thrice, what is the
Probability of getting all 3 same outcomes?
​

Answer 1

$\textbf{Given:}$

$\textsf{A fair coin is tossed thrice}$

$\textbf{To find:}$

$\textsf{The probability of getting all 3 same outcomes}$

$\textbf{Solution:}$

$\textsf{when a fair coin is tossed,}$

$\mathsf{Sample\;space,\;S=\{HHH,\;HHT,\;HTH,\;THH,\;HTT,\;THT,\;TTH,\;TTT\}}$

$\implies\mathsf{n(S)=8}$

$\textsf{Let A be the event gettting all 3 same outcomes}$

$\implies\mathsf{A=\{HHH,\;TTT\}}$

$\mathsf{Then,}$

$\mathsf{P(A)=\dfrac{\textsf{Total number of outcomes favourable to A}}{\textsf{Total number of outcomes}}}$

$\mathsf{P(A)=\dfrac{n(A)}{n(S)}}$

$\mathsf{P(A)=\dfrac{2}{8}}$

$\implies\boxed{\mathsf{P(A)=\dfrac{1}{4}}}$

$\textbf{Answer:}$

$\textsf{Probability of getting all 3 same outcomes is}\;\mathsf{\dfrac{1}{4}}$

$\textbf{Find more:}$

In a single throw of two dice,the probability of getting doublet i.e. getting the same number on both dice is(a) 1/2

(b) 1/6

(c) 1/4

(d) 1/12​

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If o is the centre of larger circle what is the probability that a point chosen at random within the circumference of the larger circle,lies outside the smaller circle ?a. 0.33

b. 0.5

c. 0.67

d.0.75

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