3.5 Probabilities Using Combinations
Chapter
Chapter 3
Section
3.5
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Solutions 22 Videos

What is the probability that a hand of five cards contains only

hearts?

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0.16mins
Q1a

What is the probability that a hand of five cards contains only

red cards?

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0.16mins
Q1b

What is the probability that a hand of five cards contains only

face cards?

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0.17mins
Q1c

In the story of the Three Little Pigs, the big bad wolf was able to blow down the two houses made of straw and of sticks, but not the house made of bricks. If the wolf chose two houses at random, what is the probability that it would be able to blow them both down?

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1.28mins
Q2

To win the grand prize in a hospital lottery, you must match SIX. different numbers chosen from the numbers 1 to 45. What is the probability of winning the grand prize?

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0.33mins
Q4

In the game of rummy, a player wins with a hand of three-of-a-kind or a run of three or more cards in the same suit. What is the probability that a hand of seven cards will be dealt

a) three kings?

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0.41mins
Q5a

In the game of rummy, a player wins with a hand of three-of-a-kind or a run of three or more cards in the same suit. What is the probability that a hand of seven cards will be dealt

b) three-of-a-kind?

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1.23mins
Q5b

In the game of rummy, a player wins with a hand of three-of-a-kind or a run of three or more cards in the same suit. What is the probability that a hand of seven cards will be dealt

the 4, 5, and 6 of spades?

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0.43mins
Q5c

In the game of rummy, a player wins with a hand of three-of-a-kind or a run of three or more cards in the same suit. What is the probability that a hand of seven cards will be dealt

a run of exactly three cards?

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2.32mins
Q5d

In the game of hearts, each of four players receives 13 cards. What is the probability that each player receives 13 cards of the same suit?

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2.07mins
Q6

Six girls and five boys wish to join a committee. Four of them will be selected. What is the probability that three girls and one boy will be selected?

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0.43mins
Q7

Four different numbers are selected at random from 1 to 15. What are the odds in favour of exactly two of the numbers being divisible by 5?

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1.24mins
Q8

spider walks from point A in its web always moving outward from the centre, until it reaches the perimeter. What 1's the probability that the spider will reach point B?

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2.17mins
Q9

Kayla is playing checkers on her smartphone. A checker is in the bottom square of the third column. It will randomly move diagonally left or right one space forward, for a total of seven moves.

a) Which space has the greatest probability as the destination for the checker?

b) If the checker begins in a different position, will it affect the results? Explain.

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2.14mins
Q10

A four—member curling team is randomly chosen from six. grade 11 students and nine grade 12 students. What is the probability that the team has at least one grade 11 student?

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0.57mins
Q11

A Plinko board has SIX. rows of pegs. The top slots are numbered 1—6. The bottom slots are labelled A—G. Contestants choose the slot into which they drop the disc. What is the best strategy for releasing the disc and for predicting its landing location?

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3.57mins
Q12

Five children are selected at random from a group of eight children. What is the probability that Fariba or Sana, but not both, is selected?

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1.42mins
Q13

Adrian has 15 classmates. He selects four of them to form a study group. What is the probability that Reg or Carlos is selected?

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1.31mins
Q14

A fast-food restaurant is running a scratch and win contest. Customers scratch six squares on a card and try to match the six numbers, randomly selected from 1 to 20, that are printed across the top of the card.

  • First prize is awarded if all six numbers match.
  • Second prize is awarded if five of the six numbers match.
  • Third prize is awarded if four of the six numbers match.

a) What is the probability of winning first prize?

b) What is the probability of winning second prize?

c) What is the probability of winning third prize?

d) What are the odds against winning a prize?

e) Predict the number of fast-food meals a person would need to buy in order to have a relatively good chance of winning a prize. Do you think this strategy is sensible? Why?

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3.47mins
Q15

In the binomial expansion of (x-y)^8, what is the probability that a randomly selected term is divisible by x^2?

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1.03mins
Q16

Three different numbers are randomly chosen from the numbers 2 to 10. What is the probability that the product is

a) even?

b) divisible by 2?

c) divisible by 6?

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1.47mins
Q17

An unknown card has been lost from a standard deck. Two cards are dealt and both turn out to be spades. What is the probability that the lost card is also a spade?

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2.19mins
Q18