action Math assist » Data analysis » Probability » Outcomes » how to discover the probability of an end result   Explanation:

If you flip a coin, the chances of you acquiring heads is 1/2. This is true every time you flip the coin so if you upper and lower reversal it 3 times, the chances of you obtaining heads every time is 1/2 * 1/2 * 1/2, or 1/8.

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Explanation:

The sample an are for rolling two six-sided dice , because each die has sides. There room three means to role a four.   The probability of rolling a four is offered by the variety of outcomes that create a four split by the total number of outcomes. Explanation:

The probability of illustration a red marble is .

The total variety of marbles is , so there are feasible outcomes. the these feasible outcomes are red marbles, so the probability the a red marble out of any marble is .

In a certain lottery, ten balls are numbered #1 v #10. 2 winning balls will certainly be drawn without replacement.

Billy dram the lottery and also picks the number 9 and also 10.

In a lottery, ten balls are numbered #1 through #10. 2 winning balls will be attracted without replacement.

Billy theatre the lottery and picks the number 9 and 10.

When flipping a coin twice, what is the probability of gaining one heads and one tails? without regard come order. I.e., one of two people the top or the tails could show up first.

Explanation:

There are 4 possible outcomes for the event HH, HT, TH, TT. Two of these four outcomes incorporate exactly one heads and one tails.

Thus the solution is 2/4 = 1/2 = 0.5

With a pair of traditional six-sided dice, what is the probability of getting a amount of much less than five OR at least ten?

Explanation:

Probability is a fraction between 0 and 1. The denominator is the total number of possible outcomes and the molecule is the total variety of desired outcomes. For two dice, the total variety of ways to role the dice is 36 (6 top top the first die deserve to go with any of the 6 top top the second die)

The adhering to outcomes result in a amount of much less than 5: 1, 1 1, 2 1, 3 2, 1 2, 2 3, 1, for 6 possible outcomes

The complying with outcomes an outcome in a sum of at least 10: 4, 6 5, 6 5, 5 6, 6 6, 5 6, 4 because that 6 possible outcomes

Since us are looking for a amount of less than five OR a amount of at the very least ten, we amount up the total variety of desired outcomes

So the probability of gaining less than 5 or at the very least ten will be 12/36, or 1/3

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### Example question #38 : Probability

There space 6 pink marbles, 3 eco-friendly marbles, and also 5 white marbles in a bag; if one marble is taken out, what is the probability that the marble is pink? Explanation:

There space 6 pink marbles out of 14 total, which reduces to 3/7.

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### Example question #39 : Probability

A fair coin is flipped three times. What is the probability that the result is top all 3 times? Explanation:

There are 8 feasible sequences that deserve to occur provided this scenario, provided as HHH, HHT, HTT, HTH, THT, THH, TTH, TTT

Only one element in this collection is the preferred outcome of 3 heads. So we gain 1/8 is our probability.

Another way to look in ~ this difficulty is to take into consideration that the probability of flipping heads once is 1/2, for this reason the probability that flipping heads 3 time consecutively is 1/2 * 1/2 * 1/2 = 1/8

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### Example inquiry #40 : Probability

A single die is rolled and one coin is flipped.

What is the probability of obtaining a number much less than 4 ~ above the die and also a top on the coin? Explanation:

To gain a number less than 4 on a die, 3/6 is the probability. To obtain a heads is a 1/2 chance.

So, since both events are independent, main point the two probabilities together to acquire your answer.

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