stats 1200 ch 4

Compute P8,6.

20160

Compute P9,9.

362880

Compute C9,3.

84

Explain why −0.41 cannot be the probability of some event. Explain why 1.21 cannot be the probability of some event. Explain why 120% cannot be the probability of some event. Can the number 0.56 be the probability of an event? Explain.

A probability must be between zero and one. A probability must be between zero and one. A probability must be between zero and one. Yes, it is a number between 0 and 1.

To determine P(A or B) means that we wish to find the probability that either A happened or B happened. We know that A and B are mutually exclusive events, so we can use the addition rule for mutually exclusive events. Note it is given that P(A) = 0.2 and P(B) = 0.3. P(A or B) = P(A) + P(B) b)Now, we are given that P(A and B) = 0.4, which, since it is possible for both events to happen at the same time, means that A and B are not mutually exclusive events. So, to determine P(A or B), we can apply the general addition rule for events. Recall that P(A) = 0.2 and P(B) = 0.3. P(A or B) = P(A) + P(B) − P(A and B)

.2+.3 =.5 b)0.2 + 0.3 − .4 =.1

What is the probability of the complement? (Enter your answer to two decimal places.)

.40

If two events A and B are independent and you know that P(A) = 0.70, what is the value of P(A | B)?

.70

Compute C10,10.

1

a) To compute P(A and B) means that we wish to find the probability that both A happened and B happened. Recall that two events are independent if the occurrence or nonoccurrence of one event does not change the probability that the other event will occur. We are given that A and B are independent events, so we can use the multiplication rule for independent events. It is also given that P(A) = 0.3 and P(B) = 0.7. P(A and B) = P(A) · P(B) b) We are given that P(A | B) = 0.8 and P(A) = 0.3. Since P(A | B) ≠ P(A), the occurrence of event B changes the probability that event A will occur. This implies that A and B are not independent Correct: Your answer is correct. seenKey not independent events. So, to determine P(A and B), we can apply the general multiplication rule for events. Recall that P(B) = 0.7. P(A and B) = P(B) · P(A | B)

a) (0.3) · .7 = .21 b) = (0.7) · 0.8 = .56

a)If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? b)Assign probabilities to the outcomes of the sample space of part (a). (Enter your answers as fractions.) Do the probabilities add up to 1? Should they add up to 1? Explain. c) What is the probability of getting a number less than 4 on a single throw? (Enter your answer as a fraction.) d) What is the probability of getting 3 or 4 on a single throw? (Enter your answer as a fraction.)

a) 1, 2, 3, 4, 5, 6; equally likely b)outcome | probability 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6 Yes, because these values cover the entire sample space. c) 3/6 = 1/2 (may be wrong) but isn't 1/3 or 1/6 d) 1/3

One professor grades homework by randomly choosing 5 out of 12 homework problems to grade. (a) How many different groups of 5 problems can be chosen from the 12 problems? (b) Probability extension: Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? (Round your answer to four decimal places.) (c) Silvia did 7 problems. How many different groups of 5 did she complete? d) What is the probability that one of the groups of 5 she completed comprised the group selected to be graded? (Round your answer to four decimal places.)

a) 792 b) .0013 c) 21 d) .0265

a) The probability the student is male or is majoring in business. b) The probability a female student is majoring in business. (c) The probability a business major is female. (d) The probability the student is female and is not majoring in business. (e) The probability the student is female and is majoring in business.

a) P(Ac or B) b) P(B | A) c) P(A | B) d) P(A and Bc) e) P(A and B)

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? b) Find P(1 on green die and 2 on red die). (Enter your answer as a fraction.) (c) Find P(2 on green die and 1 on red die). (Enter your answer as a fraction.) (d) Find P((1 on green die and 2 on red die) or (2 on green die and 1 on red die)). (Enter your answer as a fraction.)

a) yes b&c) 1/36 d) 1/18

Suppose the newspaper states that the probability of rain today is 60%. What is the complement of the event "rain today"?

no rain today