Multiplication rule Quiz 1

Question 1

A boy goes to school from Monday to Friday only if his father is in town. If his father is out of town for one day every three days, what is the probability of the boy going to school on any given day?

Accepted Answer

$$\dfrac{\text{10}}{21}$$

Answer

$$\dfrac{5}{21}$$

Answer

$$\dfrac{\text{11}}{27}$$

Answer

$$\dfrac{\text{2}}{7}$$

Question 2

A die is thrown twice. What is the probability that the product obtained is a multiple of four when 4 is not obtained on the first throw?

Accepted Answer

$$\dfrac{\text{3}}{10}$$

Answer

$$\dfrac{5}{21}$$

Answer

$$\dfrac{\text{10}}{21}$$

Answer

$$\dfrac{\text{2}}{7}$$

Question 3

5 Maths books and 7 English books are kept on a shelf, while 5 Maths books, 3 English books and 4 History books are kept on the shelf below it. A book is transferred randomly from the lower shelf to the upper shelf. If one book is taken at random from the upper shelf, what is the probability that it is a Maths book?

Accepted Answer

$$\dfrac{5}{12}$$

Answer

$$\dfrac{5}{21}$$

Answer

$$\dfrac{\text{3}}{10}$$

Answer

$$\dfrac{\text{2}}{7}$$

Question 4

While walking to the park, I saw a man standing on the footpath, carrying one bag in each hand. Bag 1, in his right hand, contained 5 gold and 7 silver coins, while bag 2 in his left hand contained 4 gold and 6 silver coins. Since I am right-handed, the probability of me using my right hand is 3/4. Standing face-to-face with the man, I took one gold coin from one of the two bags. What is the probability that the coin I took was from bag 2?

Accepted Answer

$$\text{0}\text{.4897}$$

Answer

$$\text{0}\text{.4997}$$

Answer

$$\text{0}\text{.4657}$$

Answer

$$\text{0}\text{.5057}$$

Question 5

Leander and Mahesh are playing a tennis match against each other. The match consists of five sets, and whoever wins three sets wins the match. The probability of Leander winning the first set is $$\dfrac{1}{2}$$. His probability of winning any set after losing the previous one is $$\dfrac{1}{3}$$whereas his probability of winning any set after winning the previous one is $$\dfrac{2}{3}$$, there are no ties in any set. What is the probability that Leander wins the match?

Accepted Answer

$$\dfrac{\text{1}}{2}$$

Answer

$$\dfrac{5}{21}$$

Answer

$$\dfrac{\text{10}}{21}$$

Answer

$$\dfrac{\text{2}}{7}$$