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Ten questions on probability, algebra and numbers, with answers explained as you go. Takes about 5 minutes.
Questions adapted from mathopolis.com
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Three questions to warm up.
Two balls are drawn randomly without replacement.
If the first ball drawn is green, what is the probability that the second ball is yellow?
Once the first ball is drawn and identified as green, there are now 6 balls remaining in the box, 5 of which are yellow.
Thus, P (The second ball is yellow given that the first ball is green) = 5/6
Billy randomly pulls out two socks without replacement.
If the first sock drawn is black, what is the probability that the second sock is also black, meaning Billy has a matching pair?
Once the first sock is pulled out and found to be black, there are 10 socks left in the drawer, out of which 5 are black.
So, P (The second sock is black given that the first sock is black) = 5/10 = 1/2
Eva randomly takes out a pen, returns it to the bag, and then pulls out a second pen.
If the first pen is blue, what is the probability that the second pen is red?
After taking out the first pen and finding it to be blue, because it is replaced, there are still 7 pens in total in the bag, 3 of which are red.
Therefore, P (The second pen is red) = 3/7, and the color of the first pen doesn't affect it!
Nice work so far, ___. Good luck!
C = 5/9 × (F − 32)
What is the value of C when F = 77?
If a = 3, what is the value of 7 + 5a?
Replace a with 3:
5a = 5 × 3 = 15
7 + 5a = 7 + 15 = 22
How many diamonds (in total) will appear in the next stage of the pattern?
The count of diamonds follows the sequence 2, 5, 8, 11, etc. Hence, the rule is that the count increases by 3 each time.
Consequently, the total number of diamonds in the next stage of the pattern must be 11 + 3 = 14.
Almost there, ___. Four questions to go.
[(12 + 8) ÷ (7 − 2) + 3] × 4
First, work out the parentheses: 12 + 8 = 20 and 7 − 2 = 5.
So (12 + 8) ÷ (7 − 2) = 20 ÷ 5 = 4.
Adding 3 gives 4 + 3 = 7.
Finally, multiply by 4: 7 × 4 = 28.
The digit in the hundreds place is equal to or greater than 5, thus the 3 is rounded up to 4.
So, 23,911.95 rounded to the nearest thousand is 24,000.
Calculate: 19 × 38.6 − 19 × 18.6
Recall the distributive property: a × b − a × c = a × (b − c)
Here a = 19, b = 38.6 and c = 18.6.
So 19 × 38.6 − 19 × 18.6 = 19 × (38.6 − 18.6) = 19 × 20 = 380
In the number 9,437,196, what does the 7 represent?
In 9,437,196 the 7 sits in the thousands place, so it represents 7 thousands (7,000).
1 → Super easy
6 → Really tough
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