Six coins tossed simultaneously then find the probability of getting at least 4 heads.
Six coins tossed simultaneously then find the probability of getting at least 4 heads.
Solution and Explanation
To find the probability of getting at least 4 heads when tossing six coins simultaneously, we need to calculate the probability of getting 4, 5, or 6 heads and add them together.
Probability of getting 4 heads: The number of ways to choose 4 heads out of 6 coins can be calculated as: C(6, 4) = 6! / (4!(6 - 4)!) = 15
Probability of getting 5 heads: The number of ways to choose 5 heads out of 6 coins can be calculated as: C(6, 5) = 6! / (5!(6 - 5)!) = 6
Probability of getting 6 heads: The number of ways to choose 6 heads out of 6 coins can be calculated as: C(6, 6) = 6! / (6!(6 - 6)!) = 1
Now, let's calculate the probabilities for each case:
To find the probability of getting at least 4 heads, we add these probabilities together:
Probability of getting at least 4 heads = (15 + 6 + 1) / 64 = 22 / 64 = 11 / 32
Hence, the probability of getting at least 4 heads when six coins are tossed simultaneously is 11/32 or approximately 0.34375, which is approximately 34.375%.
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Concepts Used:
Probability
Probability is defined as the extent to which an event is likely to happen. It is measured by the ratio of the favorable outcome to the total number of possible outcomes.
The definitions of some important terms related to probability are given below:
Sample space
The set of possible results or outcomes in a trial is referred to as the sample space. For instance, when we flip a coin, the possible outcomes are heads or tails. On the other hand, when we roll a single die, the possible outcomes are 1, 2, 3, 4, 5, 6.
Sample point
In a sample space, a sample point is one of the possible results. For instance, when using a deck of cards, as an outcome, a sample point would be the ace of spades or the queen of hearts.
Experiment
When the results of a series of actions are always uncertain, this is referred to as a trial or an experiment. For Instance, choosing a card from a deck, tossing a coin, or rolling a die, the results are uncertain.
Event
An event is a single outcome that happens as a result of a trial or experiment. For instance, getting a three on a die or an eight of clubs when selecting a card from a deck are happenings of certain events.
Outcome
A possible outcome of a trial or experiment is referred to as a result of an outcome. For instance, tossing a coin could result in heads or tails. Here the possible outcomes are heads or tails. While the possible outcomes of dice thrown are 1, 2, 3, 4, 5, or 6.