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8 coins are tossed simultaneously. what is the probability of getting at least 6 heads?
The Correct answer is 37/256
Explanation
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Calculate the total number of outcomes (possible arrangements of heads and tails).
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Calculate the number of favorable outcomes (arrangements with at least 6 heads).
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Divide the number of favorable outcomes by the total number of outcomes.
Steps:
a) Total number of outcomes:
This is the total number of arrangements of 8 coins, which can be heads or tails. So, there are 2 possibilities for each coin, and the total number of outcomes is:
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Total outcomes = 2^8 = 256
b) Favorable outcomes:
There are 3 combinations where you get at least 6 heads (6, 7, or 8 heads). We can calculate the number of arrangements for each combination:
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6 heads: 8C6 = 28
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7 heads: 8C7 = 8
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8 heads: 8C8 = 1
Total favorable outcomes = 28 + 8 + 1 = 37
c) Probability of getting at least 6 heads:
Probability = Favorable outcomes / Total outcomes = 37 / 256
Both methods will give you the same answer:
The probability of getting at least 6 heads = 37/256
What is Probability?
Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event will not occur, and 1 indicates that the event will definitely occur.
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In simple terms, probability can be thought of as the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes: heads or tails.
The probability of getting heads is 1/2 or 0.5, since there is one favorable outcome (getting heads) out of two possible outcomes (heads or tails).
Probability theory is a branch of mathematics that deals with calculating the likelihood of events occurring in various situations. It is widely used in fields such as statistics, economics, science, and engineering to analyze and predict the outcomes of random processes.
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Categories: Math
