The probability of the shorter piece being at least 8cm when the string is cut randomly is 0.6 or 60%. This can be calculated by dividing the length of the shorter piece by the total length of the string, which is 8cm/20cm = 0.4 or 40%. The remaining 60% represents the probability of the shorter piece being longer than 8cm.
The length of the string does not affect the probability of the shorter piece being at least 8cm. This is because the probability is determined by the relative lengths of the shorter and longer pieces, not the absolute lengths. For example, if the string was 40cm long, the probability would still be 60% as long as the shorter piece is 8cm.
No, the probability is not affected by the method of cutting the string. As long as the string is cut randomly, the probability of the shorter piece being at least 8cm will remain the same. This means that the string can be cut in any direction or with any tool, as long as it is done randomly.
No, the probability cannot be greater than 1. This is because the probability is a measure of the likelihood of an event occurring, and it cannot exceed 100%. In this case, the probability of the shorter piece being at least 8cm is already at its maximum of 60%, so it cannot be greater than 1.
The probability can be calculated for a different length of the string by using the same formula of dividing the length of the shorter piece by the total length of the string. For example, if the string is 30cm long, the probability of the shorter piece being at least 8cm would be 8cm/30cm = 0.2667 or 26.67%.