1 2 1 2 2 5

4 3

1 3 2

2 3 5

0 1 2r w

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Probability 1. Revision1). Shahida is playing ‘heads or tails’ with her friend. She spins a fair coin four times and gets four heads. a). What is the probability that she gets a tail with her next spin of the coin? b). If Shahida spins the coin 500 times in succession, approximately how many times would she expect a tail to come up?

2). The probability that Jenny will beat Gill at tennis is 2/5. The probability that Jenny will beat Gill at both tennis and snooker is 1/3 . What is the probability that Jenny will beat Gill at snooker?

3). The probability that it will rain tomorrow is r. The probability that it will be windy tomorrow is w. The probability that it will rain and be windy tomorrow is b. Both r and w are marked on the number line. Draw it and mark on a possible position for b.

4). In football, a team scores 3 points for a win, 1 point for a draw and 0 points if it loses. The probability that my team wins its next match is 0.2. The probability that it will lose the next match is 0.35. What is the probability that it will gain at least 1 point in its next match?

5). The diagram shows two fair spinners. Both are spun and the scores are added together. What is the probability that the sum of the scores is at least 7?

6). In a board game a player is given two choices to get out of jail. A - throw a coin three times. Get 2 heads and 1 tail. B - throw a die and a coin. Get a number less than 5 and a tail. The die is numbered 1 - 6. Which of the two choices should the player choose and why?

7). a). When Steven ‘Gusty Wind’ Harris plays snooker, the probability that he scores 100 points or more is 1/21. i). What is the probability he will score less than 100 points? The probability that he will score 50 points or less is 2/3. ii). Calculate the probability he scores more than 50, but less than 100 points. b). Snooker is played with 15 red balls, 6 other coloured balls and 1 white ball. All 22 are kept in a box. i). A ball is taken out at random. What is the probability that it is red? ii). This ball is put back in the box. A second ball is now taken out. Calculate the probability that both balls taken out are red.

8). Two fair, six-sided dice are thrown. A double occurs when the same number appears on both. a). How many ways can a double occur? b). What is the probability of scoring a double? c). What is the probability of scoring a total of 7 on the 2 dice? d). What is the probability of scoring either a double or a total of 7 on the two dice?

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Leave home before 08:00 08:00-08:10 after 08:10

Prob. of being late 1/501/30

1/4

No. of heads 0 1 2 TOTALFrequency 122 258 120 500

Leave home before 08:00 08:00-08:10 after 08:10Prob. of being late 0.01 0.1 0.2

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9). The probability that a woman in Bolton is at least 165 cm tall is 0.25. The probability that a woman in Bolton is colour-blind is 0.04. These probabilities are independent of each other. a). Find the probability that a woman in Bolton is both colour-blind and at least 165 cm. b). Find the probability that a woman in Bolton is less than 165 cm and not colour-blind.

10). On each day that I go to work, the probability that I leave home before 08:00 is 1/3. The probability that I leave home after 08:10 is 2/15. a). What is the probability that I leave home between 08:00 and 08:10? The probability that I am late for work depends upon the time I leave home. The probabilities are in the table below.

b). i). One day I leave home between 08:00 and 08:10 and I am not late for work. Calculate the probability that this happens. ii). What is the probability that I am not late for work?

11). Edward is asked to throw 2 coins, 500 times for homework and record the number of heads. These are his results.

a). Comment on whether you think the coins are fair. b). If the coins are fair and Edward threw them 8000 times, how many times should he expect to get at least one head?

12). A fair six-sided die is rolled. a). What is the probability of getting an odd number? b). In a game, two fair six-sided dice are rolled. The numbers on the dice are multiplied together to give the score. Calculate the probability that i). the score is an odd number, ii). the score is 7, iii). the score is 6. c). The game is played twice. What is the probability that the score is an even number in the first game and an even number in the second game?

13). On each day that I go to work, the probability that I leave home before 08:00 is 0.2. The probability that I leave home after 08:10 is 0.05. a). What is the probability that I leave home between 08:00 and 08:10? The probability that I am late for work depends upon the time I leave home. The probabilities are in the table below.

b). I have a contract to work 4000 days. Estimate how many times I would expect to be late for work during this period.

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