Question

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 42% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 12%. There is only a 52% chance that she will find a tutor at such short notice.

Answer 1

Complete Question

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 42% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 12%. There is only a 52% chance that she will find a tutor at such short notice

a What is the probability that Christine fails the course

b Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability

Answer:

a

   $P(F) = 0.264$

b

$P(T | F ) = 0.23636$

Step-by-step explanation:

From the question we are told that

The probability that Christine will fail the course if she does not have a tutor is $P(F| T') = 0.42$

The probability that Christine will fail the course if she has a tutor is $P(F| T) = 0.12$

The probability that she will find a tutor is $P(T) = 0.52$

Generally the probability that she will not find a tutor is

$P(T') = 1 - 0.52$

=> $P(T') = 0.48$

Generally the probability of failing the course is

$P(F) = P(F \ n \ T) + P(F \ n \ T')$

=> $P(F) = P(F| T) * P(T) + P(A | T') * P(T')$

=> $P(F) = 0.12 * 0.52 + 0.42* 0.48$

=> $P(F) = 0.264$

Generally if Christine ends up failing the course the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability is mathematically represented as

$P(T | F ) = \frac{ P(F | T) * P(T)}{ P(F)}$

=> $P(T | F ) = \frac{ 0.12 * 0.52}{ 0.264}$

=> $P(T | F ) = 0.23636$