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 !