Solving Questions on Compound Probability: P(A and B)

Q.

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$twice is

1. $\frac{1}{729}$

2. $\frac{8}{9}$

3. $\frac{8}{729}$

4. $\frac{8}{243}$

Q.

A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of $4$. Then the conditional probability that the score $4$ has appeared at least once is

1. $\frac{1}{3}$

2. $\frac{1}{4}$

3. $\frac{1}{8}$

4. $\frac{1}{9}$

Q.

How do you find the probability of two independent events $?$

Q.

A fair die is tossed eight times.

The probability that a third six is observed on the eight throws, is

1. $\frac{({}^{7}C_2+5^5)}{6^7}$

2. $\frac{({}^{7}C_2\times 5^5)}{6^8}$

3. $\frac{({}^{7}C_2+5^5)}{6^6}$

4. None of these

Q.

A book contains $1000$ pages numbered consecutively. The probability that the sum of the digits of the marked number of a page is $9$ is

1. $\frac{55}{1000}$

2. $0$

3. $\frac{33}{1000}$

4. $\frac{44}{1000}$

Q.

A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required. The conditional probability that $X\ge 6$ given $X>3$ equals

1. $\frac{125}{216}$

2. $\frac{25}{216}$

3. $\frac{5}{36}$

4. $\frac{25}{36}$

Q.

What is the probability of drawing $2$ yellow marbles, if the first one is NOT placed back into the bag before the second draw? There is $10$ marbles total, $2$ yellow, $3$ pink, and $5$ blue.

Q. Suppose you have a bag containing $3$ blue and $5$ red marbles. If you pick a marble at random and then pick another marble without replacing, find the probability of picking a blue marble both the times.

1. $\frac{3}{8}$
   
2. $\frac{3}{28}$
   
3. $\frac{2}{7}$
   
4. $\frac{25}{28}$
   

Q. If a four-sided die is rolled and then a six-sided die is rolled, what is the probability that they will both show the number $2$?

1. $\frac{1}{4}$
   
2. $\frac{1}{6}$
   
3. $\frac{1}{24}$
   
4. $\frac{2}{3}$
   

Q.

The probability of the spinning arrow stopping in the shaded region is $\frac{1}{2}.$

1. True
2. False

Q. A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced. Find P(red, then blue).

1. $\frac{6}{15}$
2. $\frac{5}{14}$
3. $\frac{1}{7}$

Q. A jar has $25$ yellow jelly beans and $15$ red jelly beans. If Samuel picks two jelly beans one by one without replacement at random, what is the probability that they are both red?

1. $\frac{3}{52}$
   
2. $\frac{7}{52}$
   
3. $\frac{3}{8}$
   
4. $\frac{14}{39}$
   

Q.

Two dice having six sides with numbers $1,2,3,4,5$ and $6$ written on them or rolled. answer the questions that follow.
What is the probability that sum of both numbers is less than $7$ ?

Q. What is the probability that a head is obtained, followed by a tail, if a coin is flipped twice?

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