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Sample Space
Probability
Tree Diagrams
Grids / Tables
Complementary (add to 1) and Compound Events (joint events)
100
List the sample space for tossing a coin.
H, T
100
What is the probability of tossing a tail when a normal coin is tossed?
1/2 = 0.5
100
Use a tree diagram to show the sample space for tossing two coins.
HH, HT, TH, TT
100
Use a table to show the sample space for rolling two tetrahedral dice (4 sided dice).
(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) (4,1) (4,2) (4,3) (4,4)
100
Tom wants to know what the probability is of selecting a number card from a normal deck of cards. What would the complement of this event be and what is the probability of the complement?
Complement is not a number card / a court card. P(court card) = 16/52 = 4/13
200
List the sample space for rolling a fair dice.
1, 2, 3, 4, 5, 6
200
What is the probability of getting an even number when a fair 6-sided dice is rolled?
3/6 = 1/2 = 0.5
200
Use a tree diagram to show the sample space for tossing a coin three times.
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
200
Use a table to show the sample space for rolling a fair dice and tossing a normal coin together.
(H,1) (H,2) (H,3) (H,4) (H,5) (H,6) (T,1) (T,2) (T,3) (T,4) (T,5) (T,6)
200
Use the multiplication principle to find the probability of tossing two heads in a row?
P(H,H) = 1/2 x 1/2 = 1/4
300
A card is selected from a normal deck and the suit of the card is noted. List the sample space for suit.
13 Hearts, 13 Diamonds, 13 Spades, 13 Clubs
300
A card is selected from a normal deck of cards. What is the probability of selecting a King?
4/52 = 1/13 = 0.0769
300
A bag contains 2 yellow balls and 3 pink balls. Kay picked out a ball, put it back in the bag and then picked another ball. Use a tree diagram to find the probability of getting two pink balls in a row.
4 lots of YY 6 lots of YP 6 lots of PY 9 lots of PP P(pp) = 9/25
300
A bag contains 7 green and 3 black balls. A ball is randomly selected from the bag, replaced and then another ball is selected. Use a table to calculate the probability of selecting a black ball and then a green ball.
P(B,G) = 21/100 = 0.21
300
A bag contains 7 green and 3 black balls. A ball is randomly selected from the bag, replaced and then another ball is selected. Find the probability that the first ball is black and the second is green.
P(b,g) = P(b) x P(g) = 3/10 x 7/10 = 21/100 = 0.21
400
A party bag contains 2 redskins, 5 fruit chews, 1 lollipop, and a freddo frog. List the sample space for selecting one treat from the party bag.
R, R, FC, FC, FC, FC, FC, L, FF
400
A bag in the sports store contains 5 white hockey balls, 6 red cricket balls and 4 white cricket balls. A ball is selected at random. What is the probability of selecting a white ball?
9/15 = 3/5 = 0.6
400
Use a tree diagram to find the probability of getting at least three heads when a coin is tossed four times.
P(at least 3H) = 5/16
400
Two normal dice are rolled and the sum on the faces is noted. Use a table to find the probability of rolling a sum of 7.
P(7) = 6/36 = 1/6 = 0.167
400
Four cards are selected from a normal deck of cards. After each selection, the cards are not placed back into the deck. What is the probability of selecting four picture cards in a row?
P(4 picture cards) = 12/52 x 11/51 x 10/50 x 9/49 = 3/13 x 11/51 x 1/5 x 9/49 = 297/162435 = 0.00182842
500
List the sample space for tossing two coins.
HH, HT, TH, TT
500
What has the greater probability when rolling a normal dice, getting a number greater than 3 or a number less than 5?
a number less than 5 (P=4/6)
500

A prize box contains 4 pencils and 6 erasers. As a reward for his hard work during a lesson, Tom has the opportunity to select two prizes from the box. What is the probability of Tom selecting a pencil followed by a eraser?

12 lots of pp 24 lots of pr 24 lots of rp 30 lots of rr P(pr) = 24/90 = 0.267

500
Two octahedral dice are rolled and the sum on the faces is noted. Use a table to find the probability of rolling a sum that is greater than 8.
P(sum greater than 8) = 36/64 = 0.5625
500
Three yachts, Alpha, Bravo and Charlie, often race and it is known that their probabilities of winning are 1/3, 1/2 and 1/6 respectively. A contest involving two races is held. Find the probability that Alpha does not win either race
P(w) = 1/3 and P(l) = 2/3 P(ll) = 2/3 x 2/3 = 4/9 = 0.4444