If the events A and B are mutually exclusive events such that P(A)=13(3x+1) and P(B)=14(1−x), then the set of possible values of x lies in the interval

0≤P(A)≤10≤3x+1≤3-1≤3x≤2-13≤x≤23 0≤P(B)≤10≤1-x≤4-1≤x≤3-3≤x≤10≤P(A)+P(B)≤10≤ 3x+13+1-x4≤10≤12x+3+3-3x≤120≤9x+6≤12 ⇒ -6≤9x≤6 ⇒ -23≤x≤23 ≤ x∈ -13, 23

If the events A and B are mutually exclusive events such that P(A)=13(3x+1) and P(B)=14(1−x), then the set of possible values of x lies in the interval

0≤P(A)≤10≤3x+1≤3-1≤3x≤2-13≤x≤23 0≤P(B)≤10≤1-x≤4-1≤x≤3-3≤x≤10≤P(A)+P(B)≤10≤ 3x+13+1-x4≤10≤12x+3+3-3x≤120≤9x+6≤12 ⇒ -6≤9x≤6 ⇒ -23≤x≤23 ≤ x∈ -13, 23

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If the events A and B are mutually exclusive events such that $P (A) = \frac{1}{3} (3 x + 1)$ and $P (B) = \frac{1}{4} (1 - x),$ then the set of possible values of x lies in the interval

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$[- \frac{1}{3}, \frac{5}{9}]$

$[- \frac{7}{9}, \frac{4}{9}]$

[0, 1]

$[\frac{1}{3}, \frac{2}{9}]$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{rcl} \begin{matrix} 0 \leq P (A) \leq 1 \\ 0 \leq 3 x + 1 \leq 3 \\ - 1 \leq 3 x \leq 2 \\ \frac{- 1}{3} \leq x \leq \frac{2}{3} \end{matrix} \begin{matrix} 0 \leq P (B) \leq 1 \\ 0 \leq 1 - x \leq 4 \\ - 1 \leq x \leq 3 \\ - 3 \leq x \leq 1 \end{matrix} \\ 0 & \leq & P (A) + P (B) \leq 1 \\ 0 & \leq & \frac{3 x + 1}{3} + \frac{1 - x}{4} \leq 1 \\ 0 & \leq & 12 x + 3 + 3 - 3 x \leq 12 \\ 0 & \leq & 9 x + 6 \leq 12 \Rightarrow - 6 \leq 9 x \leq 6 \\ \Rightarrow & \frac{- 2}{3} \leq x \leq \frac{2}{3} \\ \leq & x \in [\frac{- 1}{3}, \frac{2}{3}] \end{array}$