Question

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?​

Answer 1

Answer:

Given :-

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes.

To find :-

What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

Solution :-

Total number of possible outcomes = 8

P(E) = (Number of favourable outcomes/ Total number of outcomes)

(i) Total number of favourable events (i.e. 8) = 1

∴ P (pointing at 8) = ⅛ = 0.125

(ii) Total number of odd numbers = 4 (1, 3, 5 and 7)

P (pointing at an odd number) = 4/8 = ½ = 0.5

(iii) Total numbers greater than 2 = 6 (3, 4, 5, 6, 7 and 8)

P (pointing at a number greater than 4) = 6/8 = ¾ = 0.75

(iv) Total numbers less than 9 = 8 (1, 2, 3, 4, 5, 6, 7, and 8)

P (pointing at a number less than 9) = 8/8 = 1

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Answer 2

ANSWER:

• (i) P(A) = 1 / 8 = 0.125

• (ii) P(B) = 4 / 8 = 1 / 2 = 0.5

• (iii) P(C) = 6 / 8 = 3 / 4 = 0.75

• (iv) P(D) = 8 / 8 = 1

GIVEN:

• 1, 2, 3, 4, 5, 6, 7, 8 are the possible outcomes.

TO FIND THE PROBABILITY OF GETTING:

• (i) The number 8.

• (ii) An odd number.

• (iii) A number greater than 2.

• (iv) A number less than 9.

EXPLANATION:

Let S = {1, 2, 3, 4, 5, 6, 7, 8}

n(S) = 8

(i) The number 8:

Let A be the event of getting the number 8

A = {8}

n(A) = 1

P(A) = n(A) / n(S)

P(A) = 1 / 8 = 0.125

(ii) An odd number.

Let B be the event of getting an odd number.

B = {1, 3, 5 , 7}

n(B) = 4

P(B) = n(B) / n(S)

P(B) = 4 / 8 = 1 / 2 = 0.5

(iii) A number greater than 2.

Let C be the event of getting a number greater than 2.

C = {3, 4, 5, 6, 7, 8}

n(C) = 6

P(C) = n(C) / n(S)

P(C) = 6 / 8 = 3 / 4 = 0.75

(iv) A number less than 9.

Let D be the event of getting a number less than 9.

D = {1, 2, 3, 4, 5, 6, 7, 8}

n(D) = 8

P(D) = n(D) / n(S)

P(D) = 8 / 8 = 1