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Probability

Multiple Choice Questions

101.

Let X and Y represent prices (in Rs.) of a commodity in Kolkata and Mumbai respectively. It is given that $X = 65, Y = 67$

σ_X= 2.5, σ_Y = 3.5 and r(X, Y) = 0.8. What is the equation of regression of Y on X ?

Y = 0.175X – 5
Y = 1.12X – 5.8
Y = 1.12 X – 5
Y = 0.17X + 5.8

102.
In a lottery of 10 tickets numbered 1 to 10, two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers ?

$\frac{1}{15}$

$\frac{1}{2}$

$\frac{2}{15}$

$\frac{1}{5}$

$\frac{2}{15}$

Given that there are 10 lottery tickets, from which 2 tickets are drawn simultaneously.

So the all possible sets of prime numbers= (2, 3), (2, 5), (2, 7), (3, 5),(3, 7), (5, 7)

Hence probability = $\frac{Number of favourable sets}{total number of sets}$

$= \frac{6}{{}^{10}C_{2}} = \frac{6}{\frac{10 \times 9}{2}} = \frac{6}{45} = \frac{2}{15}$

103.

A committee of 3 is to be formed from a group of 2 boys and 2 girls. What is the probability that the committee consists of 2 boys and 1 girl ?

$\frac{2}{3}$
$\frac{1}{4}$
$\frac{3}{4}$
$\frac{1}{2}$

104.

A dealer has a stock of 15 gold coins out of which 6 are counterfeits. A person randomly picks 4 of the 15 gold coins. What is the probability that all the coins picked will be counterfeits ?

$\frac{1}{91}$
$\frac{4}{91}$
$\frac{6}{91}$
$\frac{15}{91}$

105.

A husband and wife appear in an interview for two vacancies for the same post. The Probability of the husband’s selection is 1/7 and that of the wife’s selection is 1/5. If the events are independent, then the probability of which one of the following is 11/35 ?