1

### 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

### 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

### 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

### 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
${5 \over 12}$