Download App

PROBABILITY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPROBABILITY1 Mark
Question
Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that only one of them will qualify the examination.
✓

Answer

Let E and F be the events that Anil and Ashima will qualify the examination, respectively.
Given that
P(E) = 0.05, P(F) = 0.10 and P(E $\cap$ F) = 0.02.
The event only one of them will qualify the examination is same as the event either (Anil will qualify, and Ashima will not qualify) or (Anil will not qualify and Ashima will qualify) i.e., E $\cap$ F´ or E´ $\cap$ F, where E $\cap$ F´ and E´ $\cap$ F are mutually exclusive
Therefore,
P(only one of them will qualify)
= P(E $\cap$ F´ or E´ $\cap$ F)
= P(E $\cap$ F´) + P(E´ $\cap$ F) - P [(E $\cap$ F´) $\cap$ P(E´ $\cap$ F)] [by general addition rule and also P [(E $\cap$ F´) $\cap$ P(E´ $\cap$ F)]= 0]
= P (E) – P(E $\cap$ F) + P(F) – P (E $\cap$ F)
= 0.05 – 0.02 + 0.10 – 0.02 = 0.11

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 1 marks)" from PROBABILITY→PROBABILITY — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A coin is tossed once Write its sample space.
→
Write $\{ X:X \in R,3 \leq X < 4\}$asinterval.
→
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die
B: getting on odd number on the first die
C: getting the sum of the numbers on the dice $\leq 5$
Describe the event 'B or C'
→
Show that two lines $a_1 x+b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$, where $b_1, b_2 \neq 0$ are: Perpendicular if $a_1 b_1+b_1 b_2=0$
→
Show that the coefficient of the middle term in the expansion of $(1 + x)^{2n}$ is equal to the sum of the coefficients of middle terms in the expansion of $(1 + x)^{2n-1}$.
→
Three coins are tossed once. Find the probability of getting: no head
→
If $A \not \subset B$ and $B \not \subset C$ , then $A \not \subset C$.If it is true, prove it. If it is false, give an example.
→
$\text{If }\cos(\text{A+B})\sin(\text{C}-\text{D})=\cos(\text{A}-\text{B})\sin(\text{C+D}),$ than write the value $\tan\text{A}\tan\text{B}\tan\text{C}.$
→
Are the following pairs of statements are negation of each other: The number x is not a rational number. The number x is an irrational number.
→
Write the component statements of the following compound statements and check whether the compound statement is true or false: To enter into a public library children need an identity card from the school or a letter from the school authorities.
→