CBSE Class 12 Mathematics Probability Case Studies

Probability

Read the following and answer any four questions. A coach is training 3 players. He observes that the player \( A \) can hit a target 4 times in 5 shots, player \( B \) can hit 3 times in 4 shots and the player \( C \) can hit 2 times in 3 shots

Question. Let the target is hit by \( A, B \): the target is hit by \( B \) and, \( C \): the target is hit by \( A \) and \( C \). Then, the probability that \( A, B \) and, \( C \) all will hit, is
(a) \( \frac{4}{5} \)
(b) \( \frac{3}{5} \)
(c) \( \frac{2}{5} \)
(d) \( \frac{1}{5} \)
Answer: (c)

Question. Referring to (i), what is the probability that \( B, C \) will hit and \( A \) will lose?
(a) \( \frac{1}{10} \)
(b) \( \frac{3}{10} \)
(c) \( \frac{7}{10} \)
(d) \( \frac{4}{10} \)
Answer: (a)

Question. With reference to the events mentioned in (i), what is the probability that 'any two' of \( A, B \) and \( C \) will hit?
(a) \( \frac{1}{30} \)
(b) \( \frac{11}{30} \)
(c) \( \frac{17}{30} \)
(d) \( \frac{13}{30} \)
Answer: (d)

Question. What is the probability that ‘none of them will hit the target’?
(a) \( \frac{1}{30} \)
(b) \( \frac{1}{60} \)
(c) \( \frac{1}{15} \)
(d) \( \frac{2}{15} \)
Answer: (b)

Question. What is the probability that at least one of \( A, B \) or \( C \) will hit the target?
(a) \( \frac{59}{60} \)
(b) \( \frac{2}{5} \)
(c) \( \frac{3}{5} \)
(d) \( \frac{1}{60} \)
Answer: (a)

Read the following and answer any four questions. In answering a question on a multiple choice test for class XII, a student either knows the answer or guesses. Let 3/5 be the probability that he knows the answer and 2/5 be the probability that he guesses. Assume that a student who guesses at the answer will be correct with probability 1/3. Let \( E_1, E_2, E \) be the events that the student knows the answer, guesses the answer and answers correctly respectively.

Question. What is the value of \( P(E_1) \)?
(a) \( \frac{2}{5} \)
(b) \( \frac{1}{3} \)
(c) 1
(d) \( \frac{3}{5} \)
Answer: (d)

Question. Value of \( P(E|E_1) \) is
(a) \( \frac{1}{3} \)
(b) 1
(c) \( \frac{2}{3} \)
(d) \( \frac{15}{4} \)
Answer: (b)

Question. \( \sum_{k=1}^{2} P(E | E_k)P(E_k) \) equals
(a) \( \frac{11}{15} \)
(b) \( \frac{4}{15} \)
(c) \( \frac{1}{5} \)
(d) 1
Answer: (a)

Question. Value of \( \sum_{k=1}^{2} P(E_k | E) \) is
(a) \( \frac{1}{3} \)
(b) \( \frac{1}{5} \)
(c) 1
(d) \( \frac{3}{5} \)
Answer: (c)

Question. What is the probability that the student knows the answer given that he answered it correctly?
(a) \( \frac{2}{11} \)
(b) \( \frac{3}{5} \)
(c) \( \frac{9}{11} \)
(d) 3
Answer: (c)