# Addition Rule (Grade 10)

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## Addition Rule

1.

In an experiment, two non-mutually exclusive events are labeled events A and B. If P(A) = 0.45, P(B) = 0.41, and P(A and B) = 0.21, what is P(A or B)?

- 0.17
- 1.07
- 0.65
- 0.25

2.

In an experiment, two non-mutually exclusive events are labeled events A and B. If P(A) = 0.33, P(A and B) = 0.12, and P(A or B) = 0.49, what is P(B)?

- 0.28
- 0.36
- 0.04
- 0.7

3.

In an experiment, two non-mutually exclusive events are labeled events A and B. If P(A) = 0.36, P(A and B) = 0.14, and P(B|A) = 0.39, what is P(A or B)?

- 0.61
- 0.22
- 0.58
- No enough information.

4.

A box contains 20 pieces of paper (all the same size) with the numbers 1 through 20 written on them. What is the probability of choosing an even number or a multiple of 3?

- 0.5
- 0.65
- 0.7
- 0.8

5.

What is the probability of selecting a black card or an even card from a standard deck of cards?

- 1/2
- 9/13
- 23/26
- 5/26

6.

A 12 sided die is color coded. Sides 1-5 are blue, sides 6-8 are green, and sides 9-12 are white. What is the probability of rolling a multiple of 3 or a side that is green?

- 1/3
- 2/3
- 7/12
- 1/2

7.

Max has been asked to sort a box of donated shoes at a thrift store. There are 6 pairs of shoes, sizes 6, 8, 8, 9, 9, and 11. If he picks out one single shoe, what is the probability that he chooses a left shoe or a size 8?

- 2/3
- 1/3
- 1/6
- 1/2

8.

Stanley works at Joe's Coffee. He has been asked to help figure out how popular Joe's Coffee's cold drinks and pastries are. Stanley looks at the receipts for the day, of which there are 150, and ignores any purchases that do not include cold drinks or pastries. He goes through them once, just looking at the first relevant item ordered, and finds that 38 people bought a cold drink and 12 people bought a pastry. Stanley then goes through the receipts again. He sees that 14 of the people who bought a cold drink also bought a pastry and 7 of the people of who bought a pastry also bought a cold drink. From this data, what is the approximate probability that someone buys a drink or a pastry at Joe's Coffee?

- 0.19
- 0.27
- 0.47
- 0.70

9.

Haley is collecting coins. She specifically likes to look for older coins or coins from other countries. Knowing this, her friend Andy decides to bring her a bag of coins he found in his grandfather's attic that nobody in his family wanted. There are 20 coins in the bag. Recently Haley read that, for most coin collections, 20% of the coins are from foreign countries and 70% are from the year 1932 and before. Assuming that this information is correct, she reasons that there are about 18 coins which she really wants (that are old or from a foreign country). Is she correct?

- Yes, she took both percentages, added them together, and then multiplied by 20.
- No, she doesn't know how many of the foreign coins are from before 1932, which would reduce the number of coins she wants to keep.
- No, she needs to multiply these percentages. Therefore, there are only about 3 coins she would want to keep.
- No, only one of the percentages applies. In order to not miss any coins she might want, she should go with the greater percentage, 70%. Therefore, she will keep about 14 coins.

10.

Jason and Eva are watching their friends play poker. They can see Josh's cards. Josh currently has four cards in his hand, and is about to receive his fifth and final card. He has the ace of clubs, two of clubs, three of clubs, and four of clubs. Jason and Eva agree that the best options for his next card would be the five of clubs, or any card in the clubs suit. Jason says that the probability of getting the five of clubs or any remaining club card is the same as simply the probability of getting any remaining club card. Eva disagrees, saying that the probability of simply getting any remaining club card would be different than the probability of getting any remaining club card or the five of clubs. Who is correct and why?

- Eva is correct, because the probability of the two events must be added together, which will be higher than the probability of either event by itself since both of these events have a probability greater than zero.
- Eva is correct, since when using the addition rule of probability, one must always add the two probabilities (in this case choosing the five of clubs and then choosing any remaining club card), and then subtract the probability that both events occur.
- Jason is correct, because the probability of choosing the five of clubs AND any remaining club card is equal to the probability of choosing the five of clubs. Using the addition rule, these cancel out and one is left with the probability of choosing any remaining club card.
- Jason is correct, since the probability of choosing the five of clubs is so low, that it can be ignored.

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