ProbabilityHardBloom L3
Question
$A,B,C$ are three events for which $P(A) = 0.4,P(B) = 0.6,P(C) = 0.5,P(A \cup B) = 0.75,P(A \cap C) = 0.35$ and $P(A \cap B \cap C) = 0.2$. If $P(A \cup B \cup C) \geq 0.75$, then $P(B \cap C)$ can take values
Options
A.0.15
B.0.2
C.0.3
D.0.4
Solution
Sol. [Key Concept: Use $P(A \cap \ B) = P(A) + P(B) - P(A \cup \ B)$ and bound $P(B \cap \ C)$.]
$$P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.25$$
$$\begin{matrix} & 0.75 \leq P(\text{ }A \cup \text{ }B \cup C) = P(\text{ }A) + P(\text{ }B) + P(C) - (P(\text{ }A \cap \text{ }B) \\ & \ + P(\text{ }B \cap C) + P(C \cap \text{ }A)) + P(\text{ }A \cap \text{ }B \cap C) \leq 1 \end{matrix}$$
$$\Rightarrow 0.1 \leq P(\text{ }B \cap C) \leq 0.35$$
Create a free account to view solution
View Solution FreeMore Probability Questions
Let A & B be two independent events of an experiment such that B is twice as likely to occur as A. If P(A) denotes the p...If two of the 64 squares are chosen at random on a chess board, the probability that they have a side in common is -...Let P (A) = 0.4 and P (B/A) = 0.5. The probability P () is equal to-...If A and B are any two events such that P (A + B) = 5/6, P (AB) = 1/3, P () =1/2, then the events A and B are-...In a maths paper there are 3 sections A, B & C. Section A is compulsory. Out of section B & C a student has to attempt a...