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14.Probability
easy
In a class of $125$ students $70$ passed in Mathematics, $55$ in Statistics and $30$ in both. The probability that a student selected at random from the class has passed in only one subject is
A
$\frac{{13}}{{25}}$
B
$\frac{3}{{25}}$
C
$\frac{{17}}{{25}}$
D
$\frac{8}{{25}}$
Solution
(a) Consider the following events :
$A = $ $A$ student is passed in Mathematics,
$B = $ $A$ student is passed in Statistics.
Then $P(A) = \frac{{70}}{{125}},$ $P(B) = \frac{{55}}{{125}},$ $P(A \cap B) = \frac{{30}}{{125}}.$
Required probability is
$P(A \cap \bar B) + P(\bar A \cap B)$$ = P(A) + P(B) – 2P(A \cap B)$
$ = \frac{{70}}{{125}} + \frac{{55}}{{125}} – \frac{{60}}{{125}} = \frac{{65}}{{125}} = \frac{{13}}{{25}}.$
Standard 11
Mathematics
