The probability of passing English Class is 667 the probabil

The probability of passing English Class is 66.7%, the probability of passing Math Class is 28.2%, and the probability of passing both of these classes is 10.4%. What is the probability of passing English or Math?                There are 36 different ways two dice will come up. What is the probability of rollong two dice that add up to 12? Enter answer as a fraction like 5/16. What is the probability that the sum of the dice will be 6?

There are 7 red rocks, 8 white rocks, and 8 blue rocks in a sack. Write all answers to the nearest 10th of a percent. What is the probability of selecting of selecting a rock that is red? What is the probability of selecting a rock, putting it back, and selecting another that are both blue? What is the probability of selecting a rock, putting it down, and selecting another that are both white? What is the probability of selecting a rock that is red, putting it down, and selecting another that is white?

Write each of these answers to 4 significant digits. You can use Scientific Notation for the answer. The probability of winning a game is 21.5% for each attempt. What is the probability that you will Not win the game (one attempt)? What is the probability that you will win the game 3 times in a row? What is the probabilty of loosing 3 in a row? What is the probability of winning at least once when the game is played 3 times in a row?

The probability of each tire on a car popping while driving is 0.7% within a 5 year time. What is the probability the the two back tires will pop in the next 5 years? What is the probability that a tire will not pop in 5 years? What is the probability that none of the tires pop in the next 5 years?

A deck of cards has 52 total cards, 1/2 black and 1/2 red. There are 4 suits; hearts, clubs, diamonds ans spades. In each suit there are 3 face cards. What is the probability of picking a random card from a shuffled deck will be a King or an Ace? What is the probability of selecting a red card or a Queen? What is the probability of selecting a Jack, putting it back, and randomly choosing another Jack? What is the probability of selecting a Queen, setting this card down, and then selecting another Queen from the deck? In other words, what is the probability of dealing yourself two Queen\'s in a row? What is the probability of selecting a Jack, setting it down, and then selecting an Ace from the deck? In other words what is the probability of dealing yourself a Jack first and then an Ace?

Solution

Solution part(a)

et The probability of passing English Class=P(E)

Given P(E)= 66.7%=0.667

let the probability of passing Math Class =P(M)

Given P(M)=28.2%=0.282

probability of passing both of these classes = P(E M)

given P(E M)=10.4%=0.104

let the probability of passing English or Math=P(EUM)

By addition theorem of probability we have

P(EUM)=P(E)+P(M)- P(E M)

=0.667+0.282-0.104

=0.845

Let the Probability that a student reads  of passing English or Math=P(EUM)\'

P(EUM)\'=1-P(EUM)

=1-0.845

=0.155

the probability of passing English or Math=15.5%

Solution part(b)

When dice is thrown, number of observations in the sample space = 6 × 6 = 36

Let A be the event that the sum of the numbers on the dice is 12

A={(6,6)}

Let P(A) be the probability for the event that the sum of the numbers on the dice is 12

=favourable outcomes /total outcomes

=1/36

Solution part(c)

Let B be the event that the sum of the numbers on the dice is 6

B={(1,5),(2,4),(3,3),(4,2),(5,1)}

Let P(B )be the probability that event that the sum of the numbers on the dice is 6

=favourable outcomes /total outcomes

=5/6²

=5/36

Solution part(d)

7 red rocks, 8 white rocks, and 8 blue rocks

Total rocks=7+8+8=23

Let the probability of selecting of selecting a rock that is red=P(R)=

7c1/23c1

=7/23

let the blue rockbe drawn in the first attempt=P(B)=8/23

now there are 7 blue rocks

and total rocks is 23 with replacement.

Therfore probability of selecting a second rock that is blue=7/23

that is selecting

the probability of selecting a rock, putting it back, and selecting another that are both blue=8/23*7/23=56/529

=0.1058=10.58%

the probability of selecting a rock, putting it down, and selecting another that are both white=8/23*7/23=56/529

=0.1058=10.58%

the probability of selecting a rock that is red, putting it down, and selecting another that is white=

7/23*8/23=56/269=0.1058=10.58%