Question

The probabilities of a student getting A, B, C and D grades are 0.35, 0.25, 0.35 and 0.05, then the probability that a student gets at most grade C is:
A) 0.35
B) 0.40
C) 0.95
D) 0.65

Answer 1

Hint:
The probability of any event happening is given by dividing the number of outcomes of that event divided by the total number of events, that is;
$P = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}$
Apply this formula, and then use the given conditions to find the required value.

Complete step by step solution:
Let us carefully read the given question and find the total number of the outcomes by adding all the given probabilities.
$
  {\text{Total number of outcomes}} = 0.35 + 0.25 + 0.35 + 0.05 \\
   = 1.00 \\
 $
Thus, in this case, we get that our total number of outcomes is 1.
We need to find the probability of the student getting at most grade C.
Thus, we first find the number of outcomes that fall under the category of “at most C”. For that, we first find the total of the probabilities of the grades A, B and C as the student could have got the grades A or B or C.
Thus,
$
  {\text{Number of Outcomes for getting atmost C}} = 0.35 + 0.25 + 0.35 \\
   = 0.95 \\
 $
We use the formula of probability given by, $P = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}$ and substitute the obtained values in it.
$
  P\left( {{\text{ atmost C}}} \right) = \dfrac{{0.95}}{{1.00}} \\
   \Rightarrow P\left( {{\text{ atmost C}}} \right) = 0.95 \\
 $

Hence, option (C) is the correct option.

Note:
In solving these types of questions, you should be familiar with the formula to find the probability of any event happening. Then use the given conditions and values given in the question, and substitute in the formula for the probability of the event, to find the missing values.