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mezya [45]
3 years ago
13

Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card an

d B be the analogous event for MasterCard. Suppose that P(A) = 0.6 and P(B) = 0.3. (a) Could it be the case that P(A ∩ B) = 0.5? Why or why not? [Hint: For any two sets A and B if A is a subset of B then P(A) ≤ P(B).]
Mathematics
1 answer:
poizon [28]3 years ago
8 0

Answer:

We have that B = 0.3.

So

0.3 = b + (A \cap B)

However, b is a probability, which means that it cannot be negative. So no, P(A ∩ B) cannot be 0.5. It can, at most, be 0.3.

Step-by-step explanation:

Event A:

Probability that a student has a Visa card.

Event B:

Probability that the student has a MasterCard.

We have that:

A = a + (A \cap B)

In which a is the probability that a student has a Visa card but not a MasterCard and A \cap B is the probability that a student has both these cards.

By the same logic, we have that:

B = b + (A \cap B)

In this problem, we have that:

A = 0.6, B = 0.3

(a) Could it be the case that P(A ∩ B) = 0.5?

We have that B = 0.3.

So

0.3 = b + (A \cap B)

However, b is a probability, which means that it cannot be negative. So no, P(A ∩ B) cannot be 0.5. It can, at most, be 0.3.

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Step-by-step explanation:

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3 years ago
You rented a car on vacation to go sightseeing for a day. You had to pay $50 for the day and $.15 per mile, along with $35 for g
stellarik [79]

The number of miles for which the car has been driven if one paid $122.50 as in the task content is; 2.5 miles.

<h3>For how many miles was the car driven?</h3>

It follows from the task content that the total amount paid was; $122.50.

Hence, after subtraction the constant charges, for the day and for gas, the remainder is;

$122.50 - $50 - $35

= $37.50.

Ultimately, if the charge per mile is $15, then the number of miles driven is; $37.50/$15

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3 0
2 years ago
Place the following in order from least to greatest. 74.6, -74.69,-74.069, 74.59
snow_lady [41]

Answer:

-74.069, -74.69, 74.59, 74.6

Step-by-step explanation:

negative numbers are smaller than positives

7 0
3 years ago
Read 2 more answers
A high school basketball coach is selecting his team. The minimum and maximum height requirements are as follows:
daser333 [38]

Answer:

B. About 2% of the boys are eligible to be a small forward on the team

Step-by-step explanation:

Recall : 1 feets = 12 inches

Point guard = 6’2" – 6’6" tall = 74 - 78 inches

Mean = 70 ; Standard deviation = 4

Z = (x - mean) / standard

P(x < 74) = (74 - 70) / 4 = 1

P(x < 78) = (78 - 70) / 4 = 2

0.97725 - 0.84134 = 0.13591

Small forward : 6'6" = 78 inches

P(x ≥ 78) = (78 - 70) / 4 = 2

P(z ≥ 2) = 0.02275 = 2.275% about 2%

Centre : 6'8" = 80

P(x ≥ 80) = (80 - 70) / 4 = 2.5

P(z ≥ 2.5) = 0.0062097 = 0.62%

8 0
3 years ago
A bag of marbles has 3 red, 4 blue, and 5 white marbles in it. What is the probability of reaching in and selecting a blue marbl
goblinko [34]

Answer:

P(B)=\frac{1}{3}

Step-by-step explanation:

The number of red marbles in the bag is; n(R)=3.

The number of blue marbles in the bag is; n(B)=4.

The number of white marbles in the bag is; n(W)=5.

The total number of marbles in the bag is: n(S)=3+4+5=12.

The probability of selecting a blue marble is P(B)=\frac{n(B)}{n(S)}

We substitute the given information to obtain:

P(B)=\frac{4}{12}

We simplify to obtain:

P(B)=\frac{1}{3}

4 0
3 years ago
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