MTH410 quiz 3

An event is _______.

An event is defined as a subset of the set of all outcomes of an experiment.

If A and B are independent events with P(A)=0.5 and P(B)=0.1, find P(A AND B).

Remember that for independent events, P(A AND B)=P(A)P(B) So, plugging in the values we are given, we find that P(A AND B)=(0.5)(0.1)=0.05

Write the first three terms of the sequence whose general term is a(n) = n!/3n

a(1)=1/3, a(2)=1/3, and a(3)=2/3

If A and B are independent events with P(A)=0.6 and P(B)=0.3, find P(A AND B).

Remember that for independent events, P(A AND B)=P(A)P(B) So, plugging in the values we are given, we find that P(A AND B)=(0.6)(0.3)=0.18

A bag contains 2 RED beads, 6 BLUE beads, and 12 GREEN beads. If a single bead is picked at random, what is the probability that the bead is RED or GREEN?

The total number of beads is 2+6+12=20. The number that are RED or GREEN is 2+12=14, so the answer is 7/10.

Given that P(B|A)=0.82 and P(A)=0.44, what is P(B AND A)? Round to three decimal places.

Remember the multiplication rule for conditional probability: P(B AND A)=P(B|A)P(A) So, plugging in the values that we know, we find P(B AND A)=(0.82)(0.44)≈0.361

A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.Drawing the Blue 2 is one of the outcomes in which of the following events?Select all correct answers.

Because the card is blue and the number is even, the card is an outcome of B and E. Therefore, it is also an outcome of R OR E and O′.

A deck of cards contains RED cards numbered 1,2,3, BLUE cards numbered 1,2,3,4,5, and GREEN cards numbered 1,2,3,4. If a single card is picked at random, what is the probability that the card is RED?

Because there are 3 red cards, and 12 cards total in the deck, the probability is 3/12

If the probability that a randomly chosen college student takes statistics is 0.70, then what is the probability that a randomly chosen college student does not take statistics? Give your answer as a decimal.

By the complement rule, the probability of NOT A is 1−P(A). Therefore, the probability that a randomly chosen college student does not take statistics is 1−0.70=0.30.

If A and B are events with P(A)=0.4, P(A OR B)=0.52, and P(A AND B)=0.08, find P(B).

First, it is helpful to write down the addition rule for probabilities: P(A OR B)=P(A)+P(B)−P(A AND B) Now, rearranging this, we find that P(B)=P(A OR B)+P(A AND B)−P(A) Plugging in the known values, we find P(B)=0.52+0.08−0.4=0.2

Let E be the event that a randomly chosen person exercises. Let D be the event that a randomly chosen person is on a diet. Identify the answer which expresses the following with correct notation: Of all the people who exercise, the probability that a randomly chosen person is on a diet.

Remember that in general, P(A|B) is read as "The probability of A given B," or equivalently, as "Of all the times B occurs, the probability that A occurs also." So in this case, the phrase "Of all the people who exercise" can be rephrased to mean "Given that a person exercises," so the correct answer is P(D|E).

Suppose A and B are mutually exclusive events, and that P(A)=0.13 and P(B)=0.85. Find P(A OR B).

Remember that when A and B are mutually exclusive events, we know that P(A AND B)=0 (this is the definition of mutually exclusive events). So for mutually exclusive events, the probability addition rule becomes P(A OR B)=P(A)+P(B)−P(A AND B)=P(A)+P(B) So we find that P(A OR B)=P(A)+P(B)=0.13+0.85=0.98

If A and B are independent events, P(A)=0.26, and P(B)=0.79, what is P(B|A)?

Since A and B are independent events, the outcome of A does not change the probability of B. So, P(B|A)=P(B)=0.79.

Which of the following shows independent events?

rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two rolls