Trifling questions-solutions before entering chapter probability

Multiple Choice: Identify the letter of the choice that best completes the statement or answers the question.

change the following probability values to fraction, decimal or percent

1. The local weather station reports that the chance of sleet is 0.99. Write this probability as a fraction and as a percent.
a. 99/100 and 99% c. 1/50 and 1%
b. 1/100 and 1% d. 99/50 and 99%
correct: a, solution:
To represent the decimal as a fraction, multiply the decimal by 100, put the result over the denominator 100 and simplify. To represent the decimal as a percent, multiply by 100, and then add the percent symbol.

2. Ross has a 79% chance of getting a black sticker out of a certain machine. Write this probability as a fraction and as a decimal.
a. 21/100 and 0.21 c. 79/50 and 0.79
b. 21/50 and 0.21 d. 79/100 and 0.79
correct: d, solution:
To represent a percent as a fraction, place the number over the denominator 100, and then simplify. To represent a percent as a decimal, divide the number by 100.

3. The chance that Rachel will win a prize is 21/50. Write this probability as a decimal and as a percent.
a. 0.42 and 42% c. 0.58 and 42%
b. 0.42 and 2.38% d. 0.58 and 58%
correct: a, solution:
To represent the fraction as a decimal, divide the numerator of the fraction by the denominator. To represent the fraction as a decimal, divide, then multiply by 100 and add a percent symbol.

fraction to percent

4. There is a ⅖ chance that Sonia will have to wash the dishes tonight. Write this probability as a decimal and as a percent.
solution:
change fraction to percent

the probability of choosing a vowel

5. A letter is chosen at random from the 26 letters in the alphabet. What is the probability of choosing a vowel?
a. 21/26 b. 26/5 c. 5/21 d. 5/26
correct: d, solution:
There are 5 vowels in the alphabet of 26 letters. So the probability is 5/26.

the probability of rolling a die

6. What is the probability of rolling a number greater than 4 on a fair number cube?
a. ⅓ b. ⅙ c. ½ d. ⅚
correct: a, solution:
There are six possible outcomes when a fair number cube is rolled. Because the number cube is fair, all outcomes are equally likely. There are two numbers greater than 4 on the number cube: 5 and 6. So the probability of rolling one of these numbers is 2/6=⅓.

7. What is the probability of rolling a number less than or equal to 5 on a fair number cube?
a. ⅚ b. ⅔ c. ⅓ d. ⅙
correct: A, solution:
There are six possible outcomes when a fair number cube is rolled. Because the number cube is fair, all outcomes are equally likely. There are five numbers less than or equal to 5 on the number cube: 1, 2, 3, 4, and 5. So the probability of rolling one of these numbers is ⅚.

the minimum number of elements picked

8. Ramu has 3 pairs of similar black socks and 4 similar pairs of blue socks. What is the minimum number of socks that he must pick out in order to ensure one full pair of similar colored socks?
A. 3 B.7 C. 9 D. 13
correct: A, solution:
There are two colored socks. So, he must pick at least three in order to ensure one pair of similar colored socks.

9. In a bag there are 4 red, 5 black and 6 yellow balls. What is the minimum number of balls that must be picked in order to ensure at least two balls of same color?
a. 3 b. 4 c. 12 d. 13
correct: b, solution:
There are three types of balls. So at least 4 balls must be picked in order to ensure at least 2 balls of 2 colors.

10. In a bag there are 4 red, 5 black and 6 yellow balls. What is the minimum number of balls that must be picked in order to ensure all the balls of at least one color?
a.3 b.4 c. 12 d. 13
correct: d, solution:
If we look the worst case scenario, then we will realise
that even after picking 12 balls, there is a possibility that are an: left with three balls each of different colours. But once, we have picked the 13th ball, at least one ball of each colour is picked.

11. In a bag there are 4 red, 5 black and 6 yellow balls. What is the minimum number of balls that must be picked in order to ensure at least one ball of each color?
a. 3 b. 4 c. 12 d. 13
correct: c, solution:
The worst case scenario is that first 6 balls are yellow, then next 5 balls are Black.
So, to ensure at least one ball of each colour 12 balls must be fetched from the bag.
Thanks for reading, lets read other!

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