Find the probability that in 5 tossing's, a perfect coin turns up Head at least 3 times in succession.
Let's consider the different possible sequences of coin tosses with the coin showing heads at least 3 times consecutively in 5 tosses:
HHHXX : In this case, we have heads for the first three tosses and either head or tail for the next two.
XHHHX: We have heads on the second, third and fourth tosses. In other words, we are allowed to have either a head or a tail in the first and last positions.
XXHHH: The third, fourth, and fifth tosses are heads, and the first two tosses can be either heads or tails.
For each scenario, the probability is:
Scenario 1: (1/2)^3 * (1/2)^2 = 1/32
Scenario 2: (1/2)^2 * (1/2)^3 = 1/32
Scenario 3: (1/2)^2 * (1/2)^3 = 1/32
Since these scenarios are mutually exclusive, we can add their probabilities to get the total probability:
Total probability = 1/32 + 1/32 + 1/32 = 3/32
So, the probability of getting at least 3 consecutive heads in 5 tosses is 3/32.
Hello,
The probability that a perfect coin turns up Head at least 3 times in succession in 5 tosses is: 3/16.
To make you concepts clear about probability, visit : https://learn.careers360.com/maths/statistics-and-probability-chapter/
Hope it helps !
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