What is the probability of each of the following?
Solution
The probability of scoring any given number when rolling one die is 1 in 6.
The probability of scoring two of any given number by rolling two dice is given by
Using the formula, a probability of at least one 2 is given by
For the second case, with three dice, it is necessary to look at the probability of each event not occurring. This is 5 in 6 for each die. So the probability of not scoring any 2s is
So the probability of scoring at least one 2 is
Allow approximately 25 minutes.
If a person tosses a coin once and rolls a die once, what is the probability that they get one head and/or one 6? Express your answer as a percentage.
The probabilities of scoring a head and rolling a six are 1 in 2 and 1 in 6, respectively, so the probability of both occurring is
Applying the formula, the probability of at least one of the two events occurring is
In other words, at least one of these events would be expected to occur on just over half the occasions. As a percentage, this is a probability of 58%.
A company manufactures bolts. The probability of a bolt having a defective thread is 2 × 10−3 (2 in 1000). The probability of a defect in the head is
2 × 10−5 (2 in 100 000).
Calculate:
2 × 10−5 × 2 × 10−3 = 4 × 10−8
This is very small indeed.
This is approximately the same as the probability of a thread defect, which is the dominant defect, so the result shouldn’t surprise you.
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