Numbers
you roll a 6 sided die and get 5 or more what is the probability
likely
What is the theoretical probability of landing heads when flipping a fair coin?
1/2
What is the term for the number of all possible outcomes?
Sample space
You flip a coin 20 times and get 14 heads. What is the experimental probability of getting heads?
70%
Let pp be a prime number greater than 3. Prove that
∑k=1p−1kp−1≡−1(modp2)k=1∑p−1kp−1≡−1(modp2)
k=1∑p−1kp−1≡−1(modp2),so the remainder is p2−1.
when a spinner is divided into 8 sections, 3 yellow, 2 red, 2 blue, 1 green. if the spinner was spun 40 times how many times would it land on blue
10 times
A standard deck has 52 cards. What is the theoretical probability of drawing a heart?
25%
What do we call an event that has no chance of occurring?
Impossible event (probability 0)
A spinner is spun 50 times, landing on green 12 times. What is the experimental probability of landing on green?
24%
Consider the quadratic equation ax2+bx+c=0ax2+bx+c=0, where aa, bb, and cc are nonzero real numbers. Suppose the roots of the equation are αα and ββ, both complex numbers, and satisfy the following system of equations:
{α+β=−ba=4,αβ=ca=5,∣α∣=∣β∣,and α3+β3=28.⎩⎨⎧α+β=−ab=4,αβ=ac=5,∣α∣=∣β∣,and α3+β3=28.
Complex
a box contains cards numbered 1 to 20. one card is selected are random, the number is recorded, and the cards is replaced. the second card is selected. what is the probibility that the first card drawn is an even number?
50%
You draw a card from a set of 12 cards where 5 are yellow. What is the theoretical probability of NOT drawing yellow?
7/12
What is the term for outcomes that have the same likelihood of occurring?
Equally likely outcomes
Out of 40 jellybeans picked randomly, 9 were blue. Predict how many blue jellybeans you’d expect in a sample of 120.
27
If I was a number what number would I be?
2
26 letters of the alphabet are written on pieces of paper and placed in a bag. if one letter is to be picked out of the bad at random find the probability is picking out J
1/26
A die is rolled twice. What is the theoretical probability of getting a “1” on both rolls?
1/36
What is the difference between theoretical probability and experimental probability?
Theoretical = probability predicted by a model (no trials). Experimental = observed frequency from actual trials/experiments
A survey of 60 students shows 18 walk to school. Based on this frequency, how many out of 300 students would you predict walk to school?
90
3+89854+4357395+45(3/9X0-38794X8384384243435)
0
A spinner has 10 equal sections numbered 1–10. What is the probability that the number spun is a prime number?
40%
A die is rolled twice. What is the theoretical probability of getting a “1” on both rolls?
75%
What is the name for a diagram used to show all possible outcomes of two-step events (like flipping two coins)?
Tree diagram (or sample-space diagram)
A die is rolled 100 times and lands on “4” exactly 9 times. Compare the experimental probability to the theoretical probability.
Experimental = 9/100=9%9/100 = 9\%9/100=9%. Theoretical = 1/6≈16.67%1/6 \approx 16.67\%1/6≈16.67%. Experimental is lower than theoretical here
prove 1+1
1