Can someone help? Please :(

A student is getting ready to take an important oral examination and is concerned about the possibility of having an "on" day or

Tamiku [17]

Answer:

The students should request an examination with 5 examiners.

Step-by-step explanation:

Let <em>X</em> denote the event that the student has an “on” day, and let <em>Y</em> denote the

denote the event that he passes the examination. Then,

$P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})$

The events ( $Y|X$ ) follows a Binomial distribution with probability of success 0.80 and the events ( $Y|X^{c}$ ) follows a Binomial distribution with probability of success 0.40.

It is provided that the student believes that he is twice as likely to have an off day as he is to have an on day. Then,

$P(X)=2\cdot P(X^{c})$

Then,

$P(X)+P(X^{c})=1$

⇒

$2P(X^{c})+P(X^{c})=1\\\\3P(X^{c})=1\\\\P(X^{c})=\frac{1}{3}$

Then,

$P(X)=1-P(X^{c})\\=1-\frac{1}{3}\\=\frac{2}{3}$

Compute the probability that the students passes if request an examination with 3 examiners as follows:

$P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})$

$=[\sum\limits^{3}_{x=2}{{3\choose x}(0.80)^{x}(1-0.80)^{3-x}}]\times\frac{2}{3}+[\sum\limits^{3}_{x=2}{{3\choose x}(0.40)^{3}(1-0.40)^{3-x}}]\times\frac{1}{3}$

$=0.715$

The probability that the students passes if request an examination with 3 examiners is 0.715.

Compute the probability that the students passes if request an examination with 5 examiners as follows:

$P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})$

$=[\sum\limits^{5}_{x=3}{{5\choose x}(0.80)^{x}(1-0.80)^{5-x}}]\times\frac{2}{3}+[\sum\limits^{5}_{x=3}{{5\choose x}(0.40)^{x}(1-0.40)^{5-x}}]\times\frac{1}{3}$

$=0.734$

The probability that the students passes if request an examination with 5 examiners is 0.734.

As the probability of passing is more in case of 5 examiners, the students should request an examination with 5 examiners.

8 0

2 years ago

Steven wants to buy a $565 bicycle. Steven has no money saved but will be able to deposit $30 into a savings account when he rec

nikdorinn [45]

Ok so he will need to have $630 to pay his sister back and buy the bike. Now do 630 divided by 30 to get 21 weeks of saving to get enough money

7 0

3 years ago

PLZ HELO FAST IM SO CONFUSED

Rasek [7]

Answer:

lol

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Hector works on the 4th floor of a high rise building. He needs to go up 9 floors to get to the cafeteria for lunch, and then go

IRINA_888 [86]

So, start at 4. You know that he needs to go up floors, so it would be 4 + 9, which is 13.
He is now on the 13th floor. You also know, that he needs to go down 5 floors. So the equation would look like this:
4 + 9 - 5 = ?
so, 13 - 5 is 8.
The meeting is on the 8th floor.

Hope this helps!!
~Kiwi

5 0

2 years ago

Use double to help you add 8+7

Aloiza [94]

You can subtract 8 -1=7 and then add 7+7=14 and then do 14+1=15 because we subtracted 1 from 8.

5 0

3 years ago