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Probability

The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.

14,643 Questions

A coin is tossed twice what is the probability that it will show heads both times?

The probability is 0.25.

Look at it this way--if you toss a coin twice, there are four equally-probable outcomes:

  • tails, tails
  • tails, heads
  • heads, tails
  • heads, heads

So the probability of heads twice in a row is one in four, or 25%.
the chance of tossing heads is 1/2 (50%) The chance of tossing the next heads is 1/2 (50%) 1/2 x 1/2 = 1/4 (25%)

Probability of two coins landing on tails?

the probabiluty of two coins landing on tails is 1/2 x 1/2 = 1/4, or one chance in four

What is approximate probability that a human offspring will be female?

50%, or half. Therefore, there is an equal chance that the offspring will be female.

How do you make a marble sorter hopper release one marble at a time?

Carefully assemble the box of marbles to the box of marbles to the box of human fecies

Why might experimental probability be different from theoretical probability?

There may not have been a sufficient number of experiments carried out.

The experiments may not have been carried out properly.

There may have been incorrect assumptions made in deriving the theoretical probability.

If you roll a die 60 times what is the probability you will roll a one or a six?

I'm assuming you're looking for the probability that you roll either a one or six at least once. So the problem can be rewritten as:

1 - probability of rolling 60 times and never getting ones or sixes

= 1 - (2/3)^60

How many ways can 9 books be arranged on a shelf so that 5 of the books are always together?

You can simplify the problem by considering it as two different problems. The first involves consider the five-book chunk as a single book, and calculating the permutations there. The second involves the permutations of the books within the five-book block. Multiplying these together gives you the total permutations.

Permutations of five objects is 5!, five gives 5!, so the total permutations are:

5!5! = 5*5*4*4*3*3*2*2 = 263252 = 14,400 permutations

Are mutually exclusive events independent?

Not necessarily. In fact, in binary situations they can be totally dependent - depends on the experiment.

Is it unusual to get a 12 when a pair of dice is rolled?

no it is not unusual to get a 12 as it is impossible to know what you will get as. it is based on a number of factors like the size of die or speed of throwing etc. so it is not unusual to get a 12

What is the probability of getting a 2 or 12 on two dice?

The probability of getting a 2 or 12 on two dice is 2 in 36, or 1 in 18.

How many ways can the 5 starting positions on s basketball team be filled with 8 men who can play any of the position?

The first position can be filled by eight, the second by seven, and so on. So the number of possibilities are:

8!/3! = 8*7*6*5*4 = 6720