Question

A student is expected to get A, B, C or D grade in a maths test. The probability of getting grade A is 0.2 and getting grade C is 0.35. The probability of getting grade B is twice the probability of getting grade D.
What is the probability of getting grade D?

a) 0.45
b) 0.30
c) 0.20
d) 0.15​

Answer 1

Given :

Expected grade are A, B, C and D

• Probability of getting grade A = 0.2
• Probability of getting grade C = 0.35
• Probability of getting grade B = 2× Probability of getting grade D

To find :

Probability of getting grade D

Solution :

We know that possible outcome are A , B, C and D

Therefore,

Probability of getting grade A + probability of getting grade B + probability of getting grade C + probability of getting grade D = 1

{ As sum of probability of all outcome will always equal to 1 }

_______________________________________________

Let -

Probability of getting grade D = x

➝ Probability of getting grade B = 2x

_______________________________________________

Total probability = 1

➝ 0.2 + 2x + 0.35 + x = 1

➝ 3x + 0.55 = 1

➝ 3x = 1 - 0.55

➝ 3x = 0.45

➝ x = 0.45 ÷ 3

➝ x = 0.15

ANSWER :

Option d) Probability of getting grade D (x) = 0.15