Directions:

A bag contains 5 yellow, 6 red, 3 white and n black balls. The probability of drawing a white ball from the bag is $\Big(\dfrac{1}{7}\Big)$.

Based on this information, answer the following questions:

51.How many black balls are there in the bag?
(a) 6
(b) 7
(c) 8
(d) 9

52.If a ball is picked at random from the bag, what is the probability that the chosen ball is not black?

(a) $\Big(\dfrac{2}{3}\Big)$

(b) $\Big(\dfrac{2}{7}\Big)$

(c) $\Big(\dfrac{4}{7}\Big)$

(d) $\Big(\dfrac{6}{7}\Big)$

53.If a ball is picked at random from the bag, what is the probability that it is either yellow or black?

(a) $\Big(\dfrac{3}{7}\Big)$

(b) $\Big(\dfrac{4}{7}\Big)$

(c) $\Big(\dfrac{6}{7}\Big)$

(d) $\Big(\dfrac{5}{14}\Big)$

54.If 5 more blue balls are added to the bag and one red ball is removed from it, what is the probability of picking up a red ball if a ball is picked up at random from the bag?

(a) $\Big(\dfrac{1}{3}\Big)$

(b) $\Big(\dfrac{1}{5}\Big)$

(c) $\Big(\dfrac{1}{6}\Big)$

(d) $\Big(\dfrac{1}{7}\Big)$

Directions:

Three unbiased coins are tossed simultaneously.

Based on this information, answer the following questions:

55.The probability of getting at least one head is:

(a) $\Big(\dfrac{3}{8}\Big)$

(b) $\Big(\dfrac{1}{2}\Big)$

(c) $\Big(\dfrac{5}{8}\Big)$

(d) $\Big(\dfrac{7}{8}\Big)$

56.The probability of getting at least two tails is:

(a) $\Big(\dfrac{1}{4}\Big)$

(b) $\Big(\dfrac{3}{8}\Big)$

(c) $\Big(\dfrac{1}{2}\Big)$

(d) $\Big(\dfrac{5}{8}\Big)$

57.The probability of getting at most two heads is:

(a) $\Big(\dfrac{1}{2}\Big)$

(b) $\Big(\dfrac{3}{8}\Big)$

(c) $\Big(\dfrac{3}{4}\Big)$

(d) $\Big(\dfrac{7}{8}\Big)$

58.The probability of getting two tails is:

(a) $\Big(\dfrac{3}{8}\Big)$

(b) $\Big(\dfrac{1}{2}\Big)$

(c) $\Big(\dfrac{3}{4}\Big)$

(d) $\Big(\dfrac{5}{8}\Big)$

Assertion (A): A bag contains 4 red, and 8 blue marbles. If a marble is drawn at random, then the probability of drawing a red marble is $\Big(\dfrac{1}{3}\Big)$.

Reason (R): Probability of an event A is given by
P(A) = $\dfrac{\text{total no. of favorable outcomes}}{\text{no. of outcomes}}$ .

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Assertion (A): A die is thrown twice. The probability of getting a bigger value on the first throw is $\Big(\dfrac{5}{12}\Big)$.

Reason (R): When we throw a die once, total number of possible outcomes is 6 and when the die is thrown twice, the total number of possible outcomes is 6 + 6 = 12.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false