Practice 2
Problems
 What is the probability of selecting a red or a blue marble from a jar with 3 red marbles, 4 green marbles, and 2 blue marbles?
 What is the probability of selecting a P or a vowel from the word PROBABILITY?
 What is the probability of selecting an I or any vowel from the word PROBABILITY?
 When you are selecting a card at random from a standard deck of 52 cards, what is the probability of selecting a king or a red card?
Solutions
 Read and understand the question. This question is looking for the probability of selecting a red or a blue marble when you are picking a marble without looking. There are 3 red marbles, 4 green marbles, and 2 blue marbles in the jar.
 Read and understand the question. This question is looking for the probability of selecting a P or a vowel from the letters of the word PROBABILITY.
 Read and understand the question. This question is looking for the probability of selecting an I or any vowel from the letters of the word PROBABILITY. There are a total of 11 letters, 2 Is, and 4 vowels, including the Is.
 Read and understand the question. This question is looking for the probability of selecting a king or a red card when you are choosing from a deck of 52 cards. There are 26 red cards and 4 kings in the deck.
Make a plan. Use the fact that there are a total of 9 marbles in the jar; 3 of them are red and 2 of them are blue. The key word or in the question tells you to add the probabilities together, and in this problem a marble cannot be red and blue at the same time, so the events are mutually exclusive.
Use the basic formula and add the probabilities together.
Carry out the plan. The formula becomes P(red or blue) The probability is equal to
Check your answer. To check this answer, substitute the values again to see if the answer is reasonable. Since 5 out of the 9 marbles are either red or blue, this is equal to the probability of This answer is checking.
There are a total of 11 letters, one P, and 4 vowels.
Make a plan. Use the fact that there are a total of 11 letters in the word; 1 of them is a P and 4 of them are vowels. The key word or in the question tells you to add the probabilities together. P is not also a vowel, so the events are mutually exclusive. Use the basic formula and add the probabilities together.
Carry out the plan. The formula becomes P(P or a vowel) =
The probability is equal to
Check your answer. To check this answer, substitute the values again to see if the answer is reasonable. Since 5 out of the 11 letters are either the letter P or a vowel, this is equal to the probability of This answer is checking.
Make a plan. Use the fact that there are a total of 11 letters in the word; 2 of them are Is and a total of 4 are vowels. The key word or in the question tells you to add the probabilities together. I is also a vowel, so the events are not mutually exclusive. Use the basic formula and add the probabilities together, but then subtract the probability of the two Is because they are also vowels.
Carry out the plan. The formula becomes P(I or any vowel)
The probability is equal to
Check your answer. To check this answer, substitute the values again to see if the answer is reasonable. Since 4 out of the 11 letters are vowels including the letter I, this is equal the probability of This answer is checking.
Make a plan. Use the facts that there are a total of 52 cards in the deck and 26 of them are red and 4 of them are kings. The key word or in the question tells you to add the probabilities together. In this problem, there are two cards that are red and a king at same time, so the events are not mutually exclusive. Use the basic formula and add the probabilities together, but subtract the probability of selecting a king that is also a red card.
Carry out the plan. The formula becomes P(red card or king)
The probability is equal to .
Check your answer. To check this answer, substitute the values again to see if the answer is reasonable. Since 28 out of the 52 cards are either red or kings, this is equal to the probability of . This answer is checking.
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