The probability increases because the variability in the sample mean increases as the sample size increases.

Does increasing sample size increase probability?

The probability of committing a Type II error is known as β . If power increases then β must decrease. So, if the power of a statistical test is increased, for example by increasing the sample size, the probability of committing a Type II error decreases.

What happens to probability distribution when sample size increases?

As sample sizes increase, the sampling distributions approach a normal distribution. With "infinite" numbers of successive random samples, the mean of the sampling distribution is equal to the population mean (µ).