Question

If a number is chosen at random from the numbers 1 to 20 inclusive, what is the probability

that:

a) a prime number will be picked? b) an even number will be picked?

c) a single digit number will be picked​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{A number is chosen at random from the numbers 1 to 20}$

$\underline{\textbf{To find:}}$

$\textsf{What is the probability that,}$

$\textsf{(a) a prime number will be picked}$

$\textsf{(b) an even number will be picked}$

$\textsf{(c) a single digit number will be picked}$

$\underline{\textbf{Solution:}}$

$\mathsf{Here,}$

$\mathsf{Sample\;space=\{1,2,3,4\;.\;.\;.20\}}$

$\implies\mathsf{n(S)=20}$

$\textsf{Let A be the event of getting a prime number}$

$\mathsf{Then,\;A=\{2,3,5,7,11,13,17,19\}}$

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

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

$\mathsf{P(A)=\dfrac{8}{20}}$

$\implies\boxed{\mathsf{P(A)=\dfrac{2}{5}}}$

$\textsf{Let B be the event of getting an even number}$

$\mathsf{Then,\;B=\{2,4,6,8,10,12,14,16,18,20\}}$

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

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

$\mathsf{P(B)=\dfrac{8}{20}}$

$\implies\boxed{\mathsf{P(B)=\dfrac{2}{5}}}$

$\textsf{Let C be the event of getting a single digit number}$

$\mathsf{Then,\;C=\{1,2,3,4,5,6,7,8,9\}}$

$\implies\mathsf{n(C)=9}$

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

$\mathsf{P(C)=\dfrac{9}{20}}$

$\implies\boxed{\mathsf{P(C)=\dfrac{9}{20}}}$

$\underline{\textbf{Find more:}}$

Let A and B be two events such that P(A)=0.6, P(B) = 0.2 and P(A/B)=0.5. Then P (A'/B')

equals

(a) 1/10

(b) 3/10

(C) 3/8

(d) 6/7​  

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