魅影直播

It is given that:

Using Conditional Probability: $P(\mathrm{B}鈭�\mathrm{A})=\frac{P(\mathrm{A}鈭�\mathrm{B})}{P(\mathrm{A})}=\frac{P(\mathrm{A}\text{and}\mathrm{B})}{P(\mathrm{A})}$

G: Good Chance

M: Male

Information about $4826$young adults is provided.

From table, $2459/4826$young adults are males.

$鈬�P\left(\mathrm{M}\right)=\frac{\text{Number of favourable outcomes}}{\text{Numberof possible outcomes}}=\frac{2459}{4826}$

Also, $78/4826$young adults have a good chance.

$P\left(\mathrm{G}\text{and}\mathrm{M}\right)=\frac{\text{Number of favourable outcomes}}{\text{Numberof possibleoutcomes}}=\frac{758}{4826}$

Using Conditional Probability

$P(\mathrm{G}鈭�\mathrm{M})=\frac{P\left(\mathrm{GandM}\right)}{P\left(\mathrm{M}\right)}=\frac{\frac{758}{4826}}{\frac{2259}{4826}}=\frac{758}{2459}鈮�0.3083=30.83\%$

Hence, $30.83\%$of young males are of the view that there is good chance for them to have much more than middle aged income at$30$and probability is$0.3083$

As per complement rule,

$P\left({\mathrm{A}}^{\mathrm{c}}\right)=P(not\mathrm{A})=1-P(\mathrm{A})$

and conditional probability $P(\mathrm{B}鈭�\mathrm{A})=\frac{P(\mathrm{A}鈭�\mathrm{B})}{P(\mathrm{A})}=\frac{P(\mathrm{A}\text{and}\mathrm{B})}{P(\mathrm{A})}$

N: Almost no chance

M: Male

From table, $194/4826$young adults think that "Almost no chance".

$鈬�4632$young adults do not have such opinion.

$P\left({\mathrm{N}}^{\mathrm{c}}\right)=\frac{\text{Numberof favourable outcomes}}{\text{Numberof possibleoutcomes}}=\frac{4632}{4826}$

From table, $96/4826$female adults have opinion "Almost no Chance".

As total female young adults are $2367$.

$鈬�2271/4826$female young adults dis not have above opinion.

$鈬�P\left({\mathrm{M}}^{\mathrm{c}}\text{and}{\mathrm{N}}^{\mathrm{c}}\right)=\frac{\text{Numberof favourableoutcomes}}{\text{Number of possible}}=\frac{2271}{4826}$

Using Conditional Probability:

$P\left({\mathrm{M}}^{\mathrm{c}}鈭�{\mathrm{N}}^{\mathrm{c}}\right)=\frac{P\left({\mathrm{M}}^{\mathrm{c}}\text{and}{\mathrm{N}}^{\mathrm{c}}\right)}{P\left({\mathrm{N}}^{\mathrm{c}}\right)}=\frac{\frac{2271}{4226}}{\frac{4632}{4826}}=\frac{2271}{4632}=\frac{757}{1544}鈮�0.4903=49.03\%$

Hence, probability for the female respondent didn't say "almost no chance" is$0.4903$