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A friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work

lubasha [3.4K]

Answer:

The probability that he drove the small car is 0.318.

Step-by-step explanation:

We are given that a friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work, and three-quarters of the time he takes the large car.

If he takes the small car, he usually has little trouble parking and so is at work on time with probability 0.7. If he takes the large car, he is on time to work with probability 0.5.

Let the Probability that he drives the small car = P(S) = $\frac{1}{4}$ = 0.25

Probability that he drives the large car = P(L) = $\frac{3}{4}$ = 0.75

Also, let WT = event that he is at work on time

So, Probability that he is at work on time given that he takes the small car = P(WT / S) = 0.7

Probability that he is at work on time given that he takes the large car = P(WT / L) = 0.5

Now, given that he was at work on time on a particular morning, the probability that he drove the small car is given by = P(S / WT)

We will use the concept of Bayes' Theorem for calculating above probability;

So, P(S / WT) = $\frac{P(S) \times P(WT/S)}{P(S) \times P(WT/S)+P(L) \times P(WT/L)}$

= $\frac{0.25 \times 0.7}{0.25 \times 0.7+0.75 \times 0.5}$

= $\frac{0.175}{0.55}$

= <u>0.318</u>

Hence, the required probability is 0.318.

8 0

3 years ago

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable

Alex_Xolod [135]

Answer:

a) Discrete, because the number of point scored during basket ball is countable.

For instance, the amount of point scored in a basketball could be 75, 103, 63 etc. The numbers are countable

b) Continuous, because the amounts of rainfall is a random variable that is uncountable.

For instance, the amount of rainfall in City Upper B during April could be 0.10 inches of rain per hour, 0.30 inches of rain per hour. This numbers are not countable, they are rather approximated or rounded off.

Step-by-step explanation:

A random variable is considered discrete if its possible values are countable while a random variable is considered to be continuous if it's possible values are not countable.

7 0

3 years ago

PLSSSS HELPPP MEEEEEE!!! I REALLY NEED HELPPP ANSWER IT CORRECTLY PLSSS

igor_vitrenko [27]

Answer:

A stem and leaf plot shouldn't be used because the numbers are more than two digits long. These numbers are more varied, so it isn't correct for a stem and leaf plot. The stem is usually the tens digit, and the leaf is the ones digit. When you have four digits, it would get infinite times more hard and complicated. Hope that helped!

6 0

3 years ago

Solve the equation log^7b>2

ahrayia [7]

Answer:

b > 12.71

Step-by-step explanation:

Here in this question we have to solve the inequality equation given for b (An unknown variable}

Now, the equation is $(\log b)^{7} > 2$