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Probability Review

Two coins are tossed simultaneously. What is the probability of tossing two heads?

A coin is tossed three times. What is the probability of tossing exactly two heads?

Two standard dice are rolled. What is the probability of rolling a total of 9?

If the odds in favour of rain tomorrow are 4:7, what is the probability of rain tomorrow?

If a bowl contains ten chocolates and eight jelly beans, what is the probability that four of the candies will be chocolates?

Two standard dice are rolled. What is the probability that a sum less than 7 is not rolled?

A stable has 15 horses available for trail rides. Of these horses, 6 are all brown, 5 are mainly white and the rest are all black. If Maria selects one at random, what is the probability that this horse will: a) be black? b) not be black?

A number is chosen randomly from the first 20 natural numbers (1 to 20). If event A = {a multiply of 5}, what is the value of P(A')?

If the odds against the Blue Jays winning this year's World Series are 20:1, what is the probability that the Blue Jays will win this series?

Describe how to calculate the odds against an event happening when you know the probability of the event occuring. Use a numerical example to illustrate your explanation.

Solution Preview

1) Two coins are tossed simultaneously. What is the probability of tossing two heads?

The sample space consists of four equally probable outcomes: HH, HT, TH, TT. The favorable event contains only one outcome, HH. So the probability of tossing two heads is 1/4

2) A coin is tossed three times. What is the probability of tossing exactly two heads?
The sample space now has 8 possible outcomes:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
Of these oucomes, HHT, HTH and THH have exactly two heads. So, the favorable event consists of 3 oucomes out of 8, and its probability is 3/8.

3) Two standard dice are rolled. What is the probability rolling a total of 9?
Let's construct the sample space. A table is usually helpful.

| 1 2 3 4 5 6
-------------------------------------------------
1 | 2 3 4 5 6 7
2 | 3 4 5 6 7 8
3 | 4 5 6 7 8 9
4 | 5 6 7 8 9 10
5 | 6 7 8 9 10 11
6 | 7 8 9 10 11 12

The leftmost column represents the numer rolled on the first dice, the topmost row contains the number rolled on the second dice.
The table contains the corresponding sums of numbers. The event that we want, E={the sum is 9}, contains ...

Solution Summary

Describe how to calculate the odds against an event happening when you know the probability of the event occuring. Use a numerical example to illustrate your explanation.

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