The Basics of Event Probability

Let's draw all the possible combinations when rolling two dice.

There are multiple combinations that add up to the same number. Remember, we cannot count an outcome multiple times. Therefore, the sample space is as follows. {2,3,4,5,6,7,8,9,10,11,12} The sample space has 11 outcomes.

To determine the probability of rolling an even number, we will highlight all even combinations in the table made earlier. Remember, an even number is divisible by 2.

We see that 18 combinations are even. Since the sample space is 6 by 6, the total number of possible combinations is 6* 6= 36. Now we can calculate the probability by dividing the number of favorable combinations by the number of possible combinations. P=18/36= 1/2 The probability of rolling an even number is 12.

Let's list all of the dice combinations that give a difference of 3. & Die 1-Die 2 [-1.1em] &D1 - D2 = 4-1 = 3 &D1 - D2 = 5-2 = 3 &D1 - D2 = 6-3 = 3 [1em] & Die 2-Die 1 [-1.1em] &D2 -D1 = 4-1 = 3 &D2 -D1 = 5-2 = 3 &D2 -D1 = 6-3 = 3 Let's highlight all of these combinations in the table we made earlier.

Of the 36 possible combinations, 6 of them give a favorable outcome. Now we can calculate the probability that the difference between the dice is 3. P=6/36= 1/6

The most likely outcome is the number in the sample space that occurs most frequently. If we again look at the table with all the possible combinations for the dice, we see that 7 is the most frequent outcome.

There are 6 different combinations that give a seven. With this information, we can calculate the probability of rolling this outcome. P=6/36= 1/6

From the exercise, we know that of the 2000 computers tested, 8 have defects. If we divide the number of defective computers by the total number of tested computers, we get the probability of a computer having a defect.

Consequently, there is a 0.4 % chance that a computer picked at random has a defect.

To predict the number of computers with defects in a shipment of 100 000, we must multiply the probability found earlier by the number of computers in the shipment. 100 000(0.004)=400 About 400 computers in the shipment could be defective.

A standard deck has 52 playing cards. Therefore, the number of possible outcomes when drawing a card from one is 52.

In this case, we have a coin and a bag of marbles. A coin has two outcomes, heads and tails. This produces two outcomes.

Next up, we have to choose a marble. This can be purple or gold. Notice that we are not concerned with probabilities to figure out the possible outcomes. Only the number of possible outcomes is important, which means we will disregard the fact that there are more purple marbles than gold marbles in the bag.

Therefore, the number of possible outcomes in the sample space is 4. {H, P}, {H, G }, {T, P}, {T, G}

As in the previous situation, we are not concerned with probabilities at this point. Rather, we want to list all the possible outcomes. We can make another tree diagram to show all the possibilities.

As we can see, we have a total of 8 possible outcomes. {G, B, B}, {G, B, G}, {G, G, B}, {G, G, G}, {B, B, B}, {B, B, G}, {B, G, B}, {B, G, G}

To calculate the probability of an event, we have to divide the number of favorable outcomes by the number of possible outcomes. P=Number of favorable outcomes/Number of possible outcomes In this case, Jordan has a regular six-sided die and we want to find the probability of her rolling at least a 2. This means we cannot roll a 1.

We have 5 favorable outcomes of 6 possible outcomes. Now we can determine the probability. P(At least a2)=5/6

Let's find all the possible even outcomes on a die.

We have 3 favorable outcomes out of 6 possible outcomes. Now we can determine the probability. P(Even)=3/6=1/2

Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes. P=Number of favorable outcomes/Number of possible outcomes We have 4 blue balls, 3 red balls, and 5 yellow balls. blue balls:& && 4 red balls:& && 3 yellow balls:& && 5 [-1.2em] total:& &&12 We want to know the probability of picking a blue ball. With the given information, we can determine the probability of picking a blue ball. P( Blue) = 4/12=1/3

This time, we must divide the sum of the blue and yellow balls by the total number of balls. From the previous section we know that 4 balls are blue and 5 are yellow, for a total of 9 balls. Now we can determine the probability. P(BlueorYellow) = 9/12=3/4 The probability of picking a blue or a yellow ball is 34.

The event of picking a ball that is neither blue nor yellow is the complement of picking a blue or yellow ball. We already calculated the probability of picking a blue or yellow ball in the previous section. P(Blue or Yellow) = 3/4 Therefore, the probability of picking a ball that is neither blue nor yellow can be found using the complement rule.

The probability of picking a ball that is neither blue nor yellow is 14.

Let's think about the statements one at the time.

i. A Person With a High Income Went to College

A person does not have to have gone to college to have a high income. However, it still increases the possibility of securing a high-paying job if they have. The most appropriate probability would be 0.7. This is completely arbitrary, by the way — someone can definitely succeed without having gone to college!

ii. An Ant Can Fly a Jet

Ants are not able to fly a jet created for a human. The probability of this is therefore 0.

iii. A Card Dealer Deals the Ace of Spades

The ace of spades is one card out of 52 cards in a standard deck. To calculate the probability of being dealt this card, we divide 1 by 52. P=1/52≈ 0.02 The probability is about 0.02.

iv. Flipping a Coin Gives Either Heads or Tails

There are two possible outcomes when we flip a coin, either heads or tails. Therefore, the probability of either of them happening must be 1.

If the person does not win $10, they will have drawn either a no prize ticket or a $20 prize ticket. They therefore have the following complement. $20 prize and No prize