Question

Probablity question

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{A man and woman appear in an interview for 2 vacancies}\hspace{.33em}\\~\\
& \normalsize \text{of same post.The probablity of man's selection is }\ \dfrac{1}{4} \text{and that of } \hspace{.33em}\\~\\
& \normalsize \text{woman's selection is }\ \dfrac{1}{3}\ \text{What is the probablity that none } \hspace{.33em}\\~\\
& \normalsize \text{of them will be selected} \hspace{.33em}\\~\\
& a.)\ \dfrac{1}{2} \hspace{.33em}\\~\\
& b.)\ \dfrac{1}{3} \hspace{.33em}\\~\\
& c.)\ \dfrac{2}{5} \hspace{.33em}\\~\\
& d.)\ \dfrac{3}{7} \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

same thing, use the fact that the events are independent :
\[P(A'\cap B') = P(A')\times P(B')\]

Answer 3

is it also \([1-P(\text{both will be selected)}]\)

Answer 4

hint:
If 1/4 is P(selected), so \((1-\frac{1}{4})\) is P(not selected). Similarly for the woman.

Answer 5

nope, you need to subtract probabilities for exactly one of them is selected too

Answer 6

all that is a pain in the neck, so just use mathmate's hint

Answer 7

matemate what is ur full hint

Answer 8

and since they are independent events the probabilities are multiplied

Answer 9

My hint is just a follow-up to yours, lol.
@ganeshie8

Answer 10

oh so it's same

Answer 11

1/2

Answer 12

Use the formula given by @ganeshie8
My hint is to help you find P(A') and P(B').
A' is the complement of A.
For example, A=P(selected)=1/4, then A'=P(not selected)=1-1/4=3/4.
So do this for both man and woman, and use @ganeshie8 's hint.

Answer 13

is it 1/2 final answer

Answer 14

How did you arrive at 1/2? Please show us some details to make sure.

Answer 15

\(\large \color{black}{\begin{align}
P(A'\cap B') &= P(A')\times P(B')\hspace{.33em}\\~\\
&= (1-P(A))\times (1-P(B))\hspace{.33em}\\~\\
&= (1-1/4)\times (1-1/3)\hspace{.33em}\\~\\
&= (3/4)\times (2/3)\hspace{.33em}\\~\\
&= (1/2)\hspace{.33em}\\~\\
\end{align}}\)

Answer 16

looks good to me!

Answer 17

thnks

Answer 18

just for more practice, maybe try working the probability using ur initial method

Answer 19

is it also \([1-P(\text{both will be selected)}]\)

Answer 20

as i said earlier, that is wrong, here is the correct one :

\(\begin{align}P(\text{none selected})&=1-P(\text{both will be selected)}\\&-P(\text{man selected, woman not selected)}\\ &- P(\text{man not selected, woman selected)}\end{align} \)