Question

NO LINKS!! NOT A MULTIPLE CHOICE. PART 4 Please help​

Answer 1

Answers are in bold

4a)  13/49

4b)  32/245

4c)  22/49

4d)  37/49

4e)  213/245

5)  0 and 1

6)  They must sum to 1

===========================================================

Explanation:

4a)

Add up all the numbers in the frequency column.

50+65+32+38+60 = 245

Then divide the frequency for ground beef (65) over the total (245)

65/245 = 13/49 is the probability of getting ground beef

--------------------------------------

4b)

Divide the frequency for bacon (32) over the total calculated earlier.

The probability of getting bacon is 32/245

The fraction cannot be reduced further since 32 and 245 don't have any factors in common other than 1.

--------------------------------------

4c)

50 people bought boneless chicken and 60 bought pork tenderloin.

This sums to 50+60 = 110 people out of the 245

110/245 = 22/49 is the probability of someone getting either boneless chicken or pork tenderloin.

--------------------------------------

4d)

60 bought pork tenderloin out of the 245 total. That leaves 245-60 = 185 who did not buy pork tenderloin

185/245 = 37/49 is the probability of someone not getting pork tenderloin.

--------------------------------------

4e)

32 people bought bacon out of the 245 people total. This means 245-32 = 213 people did not buy bacon.

The probability of not buying bacon is therefore 213/245. The fraction cannot be reduced further.

--------------------------------------

5)

Probabilities must always be between 0 and 1.

0 represents "the event is impossible and will never happen"

1 represents "the event is guaranteed to happen"

In other words, 0 represents a 0% chance of it happening, while 1 represents a 100% chance of it happening.

If x is the probability of some event, then $0 \le x \le 1$

--------------------------------------

6)

The probabilities must sum to 1.

In other words, all the probabilities must add to 1.

Like mentioned earlier, the value 1 in terms of probability represents 100%

It's like adding fractions of a pizza and those fractions must add up to a whole pizza. We cannot add past 100% because this is the highest we can go.

Answer 2

Answer:

$\begin{tabular}{| c | c |}\cline{1-2} \bf Meat Type & \bf Frequency\\\cline{1-2} Boneless chicken & 50 pounds\\\cline{1-2} Ground beef & 65 pounds\\\cline{1-2} Bacon & 32 pounds\\\cline{1-2} Turkey sausage & 38 pounds\\\cline{1-2} Pork tenderloin & 60 pounds\\\cline{1-2} \bf Total & \bf 245 pounds\\\cline{1-2}\end{tabular}$

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Part (a)

$\textsf{P(Ground beef)}=\sf \dfrac{65}{245}=\dfrac{13}{49}$

Part (b)

$\textsf{P(Bacon)}=\sf \dfrac{32}{245}$

Part (c)

$\textsf{P(Pork tenderloin)}=\sf \dfrac{60}{245}$

$\textsf{P(Boneless chicken)}=\sf \dfrac{50}{245}$

$\implies \textsf{P(Pork tenderloin) or P(Boneless chicken)}=\sf \dfrac{60}{245}+\dfrac{50}{245}=\dfrac{110}{245}=\dfrac{22}{49}$

Part (d)

$\begin{aligned}\textsf{P(not Pork tenderloin)} & =1-\textsf{P(Pork tenderloin)}\\& = \sf 1-\dfrac{60}{245}\\& = \sf \dfrac{37}{49}\\\end{aligned}$

Part (e)

$\begin{aligned}\textsf{P(not Bacon)} & =1-\textsf{P(Bacon)}\\& = \sf 1-\dfrac{32}{245}\\& = \sf \dfrac{213}{245}\\\end{aligned}$