# Answer the following questions with an explanation?

##### 1 Answer
Nov 24, 2016

Please see below.

#### Explanation:

(1) - As pack contains cards numbered $1$ to $20$, if a card is selected at random, all have equal probability of being selected and probability of each is $\frac{1}{20}$. As such probability of getting $6$ is $\frac{1}{20}$. We get a multiple of $3$, when we get $\left\{3 , 6 , 9 , 12.15 .18\right\}$ and hence probability of getting a multiple of $3$ is $\frac{6}{20} = \frac{3}{10}$. Prime numbers between $1$ and $20$ are $\left\{1 , 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19\right\}$ and hence probability of getting prime numbers is $\frac{9}{20}$. It is apparent from this that probability of not getting a prime is $\frac{11}{20}$.

(2) As book is page numbered $1$ to $45$, odd numbers will appear on left hand side and even on right hand side and it could open at 1 or 2-3 or 4-5 and so on and lastly 44-45 - $22$ possibilities. $3$ will appear when we get 2-3, 12-13, 22-23, 30-31, 32-33, 34-35, 36-37, 38-39 and 43-44 and probability of appearing a page number containing $3$ will be $\frac{9}{22}$.

(3) As probability of getting a blue marble is $\frac{1}{2}$ and getting a red marble is $\frac{1}{3}$, the probability of getting a yellow marble is $1 - \frac{1}{2} - \frac{1}{3} = \frac{1}{6}$

(4) As among red and blue beetles, there is a 75%=3/4 probability of randomly selecting a red beetle and there are $24$ red beetles, we have 100%-75%=25% blue beetles and there number will be $\frac{24}{3} = 8$ (as 25% is one-third of 75%) and we have $24 + 8 = 32$ beetles altogether.

(5) As the cards are numbered 1 to 9 and there are 9 possibilities, getting less than 8 means getting 1 to 7 and probability of Arun getting it is $\frac{7}{9}$. Sally loses if she gets less than 6 on die and as a die contains six faces numbering 1 to 6, probability of Sally loosing is $\frac{5}{6}$ and she has $\frac{1}{6}$ chance of winning. Hence, Arun has greater chance of winning game.