Introduction to Probability

Q.

Write all the possible $3$ digit numbers formed from $5,3,4$ if digits can be repeated.

Q. A $6$-sided die is rolled. What is the probability of rolling a number less than $8$?

Q.

Mr. Adams has $14$ boys and $8$ girls in his mathematics class. If he chooses two students at random to work on the board, what is the probability that both students chosen are boys?

Q. The probability of a number chosen randomly from the numbers $1,2,3,...12$ being a prime number is

1. $\frac{1}{2}$
2. $\frac{1}{3}$
3. $\frac{5}{12}$
4. $\frac{2}{3}$

Q. A glass jar contains $30$ red marbles. If a single marble is chosen at random from the jar, what is the probability that it is a blue marble?

1. $1$
2. $\frac{1}{30}$
   
3. $30$
4. $0$

Q. Which among the following is/are the cause(s) of uncertainity when we evaluate probability?

1. Information occurred from unreliable sources
2. Experimental errors
3. Equipment fault
4. Temperature variation
5. Climate change

Q. From the digits $36,37,\dots 50,$ a digit is selected at random. Choosing an even number has a probability

1. 
   $\frac{7}{15}$
2. 
   $\frac{8}{15}$
3. 
   $\frac{6}{15}$
4. 
   $\frac{9}{14}$

Q. The probability of obtaining a head and a tail simultaneously when we toss a coin is