A fair coin is tossed 30 times What is the probability that the coin will show heads fewer than 17 times?

Question

Hazel Anglin · Accepted Answer

#p_(<16 heads) = 0.5 + 0.1406= 0.6406#

Since in this problem

#barx>=15 and p = 0.5#

It can be solved using Binomial Approximation to Normal Distribution.

[Using the Binomial Distribution as such and find the individual probabilities and finding the sum is a very tedious process]

Mean #barx = np = 30 xx 0.5=15#
[It is a fair coin, so #p=0.5 and q=0.5]#

#sigma = sqrt(npq)=sqrt(30xx0.5xx0.5)=2.74#
#z=(x-barx)/sigma=(16-15)/2.74=0.36#

In the given figure area under Normal Curve gives the total probability.

The required probability is yellow colour area.

Yellow colour area = area to the left of mean (i.e., 15) + area between 15 and 16.

The #z# value for #16 # is already calculated.

It is #0.36#

Using the area under Normal Curve Table find the Probability value for #0.36#

It is #0.1406#

Probability value represented by the area to the left of Mean is #0.5#

Hence -

#p_(<16 heads) = 0.5 + 0.1406= 0.6406#

Jace Anderson · Answer

undefined To find the probability that a fair coin will show heads fewer than 17 times out of 30 tosses, you can use the binomial probability formula. This formula calculates the probability of getting a certain number of successes (in this case, heads) in a fixed number of trials (the 30 coin tosses), given the probability of success on each trial (0.5 for a fair coin).

Using a calculator or statistical software, you can calculate this probability by summing the probabilities of getting 0, 1, 2, ..., 16 heads out of 30 tosses. The cumulative probability of getting fewer than 17 heads is the sum of these individual probabilities.