1
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are $${3 \over 4},{1 \over 2}$$ and $${5 \over 8}$$ respectively, then the probability that the target is hit by P or Q but not by R is :
A
$${{21} \over {64}}$$
B
$${{9} \over {64}}$$
C
$${{15} \over {64}}$$
D
$${{39} \over {64}}$$
2
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
A
$${{255} \over {256}}$$
B
$${{127} \over {128}}$$
C
$${{63} \over {64}}$$
D
$${{1} \over {2}}$$

Explanation

An unbiased coin is tossed 8 times which is same as 8 coins tossed 1 times.

$$\therefore\,\,\,$$ Possible no. of out come = 28

$$\therefore\,\,\,$$ Sample space = 28

Here in this condition, all head or all tail out come is not acceptable.

No. of times all head can occur

(H H H H H H H H) = 1

$$\therefore\,\,\,$$ Probability (all head) = $${1 \over {{2^8}}}$$ = $${1 \over {256}}$$

No. of times all tail can occur

(T T T T T T T T) = 1

$$\therefore\,\,\,$$ Probability (all tail) = $${1 \over {{2^8}}}$$ = $${{1 \over {256}}}$$

$$\therefore\,\,\,$$ Required probability

= 1 $$-$$ (P (All head) + P (All tail))

= 1 $$-$$ ( $${{1 \over {256}}}$$ + $${{1 \over {256}}}$$)

= 1 $$-$$ $${{1 \over {128}}}$$

= $${{127} \over {128}}$$
3
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :
A
$${{21} \over {220}}$$
B
$${{3} \over {11}}$$
C
$${{1} \over {11}}$$
D
$${{2} \over {23}}$$
4
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

Let E and F be two independent events. The probability that both E and F happen is $${1 \over {12}}$$ and the probability that neither E nor F happens is $${1 \over {2}}$$, then a value of $${{P\left( E \right)} \over {P\left( F \right)}}$$ is :
A
$${4 \over 3}$$
B
$${3 \over 2}$$
C
$${1 \over 3}$$
D
$${5 \over 12}$$

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