Mathematics - Probability

-PROBABILITY =

Number of POSSIBLE EVENT

---

Number of TOTAL OUTCOME

 

Question 1

Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw?

Options

A) ⅔

B) ½

C) ⅓

D) ¼

Solution:

In a football game, one team either wins or there is a tie. This means there are three possible outcomes: a win, a loss or a draw. Therefore, the probability of a draw is ⅓

The correct answer is C.

Question 2

Given distribution of color beads: blue, black, yellow, white and brown with frequencies 1, 2, 3, 4 and 5 respectively. Find the probability that a bead picked at random will be blue or white.

Options

A) 7/15

B) 2/5

C) 1/3

D) 1/15

Solution:

Total number of beads = 15.

Number of white beads = 4.

⇒P(white) = 4/15

Number of blue beads = 1.

⇒P(blue) = 1/15

P(white or blue) = P(white) + P(blue) =5/15

🔶P(white or blue) = ⅓

The correct answer is C.

Question 3

A die is rolled, find the probability that an even number is obtained.

Options

A. ⅙

B. ¼

C. ⅓

D. ½

Solution:

Let us first write the total outcome T of the experiment.

T = {1,2,3,4,5,6}

Let E be the possible event "an even number is obtained" and write it down.

E = {2,4,6}

We now use the formula of  probability.

P(Even no) = n(E) / n(T)

P(Even no) = 3 / 6 = ½

The correct Answer is D.

Question 4

Two coins are tossed, find the probability that two heads are obtained. Note: Each coin has two possible outcomes H (heads) and T (Tails).

Options

A. 1

B. ¼

C. ½

D. 2

Solution:

The total outcome T is given by.

S = {(H,T),(H,H),(T,H),(T,T)}

Let E be the possible event "two heads are obtained".

E = {(H,H)}

We use the formula of probability.

P(E) = n(E) / n(T) = ¼

The correct Answer is B.

Question 5

Which of these numbers cannot be a probability?

A) -0.00001

B) 0.5

C) 0

D) 1.001

Solution

A probability is always greater than or equal to 0 and less than or equal to 1, hence option A cannot represent probabilities: -0.00010 is less than 0

The correct answer is A.