1
KCET 2021
MCQ (Single Correct Answer)
+1
-0

Given that, $$A$$ and $$B$$ are two events such that $$P(B)=\frac{3}{5}, P\left(\frac{A}{B}\right)=\frac{1}{2}$$ and $$P(A \cup B)=\frac{4}{5}$$, then $$P(A)$$ is equal to

A
$$\frac{3}{10}$$
B
$$\frac{1}{2}$$
C
$$\frac{1}{5}$$
D
$$\frac{3}{5}$$
2
KCET 2021
MCQ (Single Correct Answer)
+1
-0

If $$A, B$$ and $$C$$ are three independent events such that $$P(A)=P(B)=P(C)=P$$, then $$P$$ (at least two of $$A, B$$ and $$C$$ occur) is equal to

A
$$P^3-3 P$$
B
$$3 P-2 P^2$$
C
$$3 P^2-2 P^3$$
D
$$3 P^2$$
3
KCET 2021
MCQ (Single Correct Answer)
+1
-0

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

A
$$\frac{1}{18}$$
B
$$\frac{5}{18}$$
C
$$\frac{1}{5}$$
D
$$\frac{2}{5}$$
4
KCET 2021
MCQ (Single Correct Answer)
+1
-0

A car manufacturing factory has two plants $$X$$ and $$Y$$. Plant $$X$$ manufactures $$70 \%$$ of cars and plant $$Y$$ manufactures $$30 \%$$ of cars. $$80 \%$$ of cars at plant $$X$$ and $$90 %$$ of cars at plant $$Y$$ are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant $$X$$ is :

A
$$\frac{56}{73}$$
B
$$\frac{56}{84}$$
C
$$\frac{56}{83}$$
D
$$\frac{56}{79}$$
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