Question

Question 1

Select one answer.

Let A and B be two independent events. If P(A) = 0.5, what can you say about P(A | B)?

1. Cannot find it because P(B) is not known.
2. Cannot find it because P(A and B) is not known.
3. Cannot find it because both P(B) and P(A and B) are not known.
4. It is equal to 0.5.
5. It is equal to 0.25.

Question 2

Select one answer.

Suppose a basketball team had a season of games with the following characteristics:

• Of all the games, 60% were at-home games. Denote this by H (the remaining were away games).

• Of all the games, 25% were wins. Denote this by W (the remaining were losses).

• Of all the games, 20% were at-home wins.

Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.)

1. 0.12
2. 0.15
3. 0.20
4. 0.33
5. 0.42

Question 3

Select one answer.

Suppose your friends have the following ice cream flavor preferences:

• 70% of your friends like chocolate (C). The remaining do not like chocolate.

• 40% of your friends sprinkles (S) topping. The remaining do not like sprinkles.

• 25% of your friends like chocolate (C) and also like sprinkles (S).

If your friend had chocolate, how likely is it that they also had sprinkles? (Note: Some answers are rounded to 2 decimal places).

1. 0.10
2. 0.18
3. 0.28
4. 0.36
5. 0.63

Question 4

Select one answer.

Suppose that the handedness of the last fifteen U.S. presidents is as follows:

• 40% were left-handed (L)

• 47% were Democrats (D)

• If a president is left-handed, there is a 13% chance that the president is a Democrat.

Based on this information on the last fifteen U.S. presidents, is “being left-handed” independent of “being a Democrat”?

1. Yes, since 0.40 * 0.47 is not equal to 0.13.
2. No, since 0.47 is not equal to 0.13.
3. Yes, since 0.47 is not equal to 0.13.
4. No, since 0.40 is not equal to 0.13.

Question 5

Type numbers in the boxes.

If P(A) = 0.8, P(B) = 0.49, and P(A and B) = 0.07, then P(A|B) =(_____) .

(Please round to two decimal places.)

Question 6

Type numbers in the boxes.

If P(A) = 0.22, P(B) = 0.86, and P(A or B) = 0.91, then P(A|B) = (______) .

(Please round to two decimal places.)

Question 7

Type numbers in the boxes.

A hair salon surveyed 247 customers (114 females and 133 males) to see if they are satisfied with the service. The result is summarized in the following table.

Satisfied Not Satisfied Total Female 97 17 114 Male 107 26 133 Total 204 43 247

1. If a customer is randomly selected from these 247 people, the probability that he/she is satisfied is(___) .

(Please round your answer to two decimal places.)

2. If we know the selected customer is a female, then what is the probability that she is satisfied?

(Please round your answer to two decimal positions.)

P(satisfied|female) =(__________)

3. How about the probability that a randomly selected customer is a female if we know that the person is satisfied?

(Please round your answer to two decimal positions.)

P(female|satisfied) = (_________)

Question 8

Select one answer.

At a dental office, the probability a patient needs a cleaning is 0.6. The probability a patient needs a filling is 0.33. Assuming the events "needs a cleaning" and "needs a filling" are independent, then what is the probability a patient needs a filling given that he/she needs a cleaning?

1. 0.2
2. 0.33
3. Additional information is required to determine the probability.
4. 0.43
5. 0.6

Answer 1

solution 1 Here the A and B are independent so P(A and B) = P(A) P/B) - 3o P(A/A) = P(A) P(A) = 0.5 (optionid) Given that :- P(w) = 25 100 of all the games 20% were at Home wins i.e., P(WAH) = 20 P(WAH)+ P(WSOH) = PCH) P (WAH) + P(W1 HC.) = P(W. So, probability of = P(WOH) PCH) 20 0:33 Ception d) //

Given that : PLC) = 70% - 0.70 P(S) = 40% = 0.40 P(ans) - 25% = 0.25 Hence, there requised probality is, P(X) = p (snc) PC) 0-25 0.7 P(3/):-(0-36(option o) Griven that: 40% wese left-handed (2) 47% were Democsats (0) If a president is left-handed, there is a 13% chance that the president is a Democrat. PO) = P(PL) P(D)= 0.47, P(O/)=0-13 Hese. 0.47 not equal to 0-13 , they are not independent. NO, Since' 0.47 is not equal to 0-13 -> (option B),

(05) Given that: P(A) =0.8 P(B) 20:49 P(ANB) - 0.07 :: P(A/B) = P(ANB) P(B) 0.07 0.49 P(A/B) - 0.142), (98) Given that P(A) = 0.22 PB):0.86 P (AUG) - 0.91 P(AUB) = P(A) + P(Ⓡ)- P(and) 0.91-0-22+0.86 - P(ANB) PCANB) = 0.17 P(A/B) = P(ANB) : 6986 P(B) 0.86 0.86 P(A/B) = 10.197, X