Ans.
P(E)= TotalOutcomes / FavorableOutcomes
There are two possible outcomes for each toss, P= 1/2
And there are 5 total tossed, n= 5
So,
(i) The probability of getting no heads in a single coin toss is 1/2 (tail).
The probability of getting no heads in five coin tosses is 1/2*1/2*1/2*1/2*1/2 = 1/32.
(ii) The probability of getting at least one head in five coin tosses can be found by subtracting the probability of getting no heads from 1.
1-(1/32) = 31/32.
(iii) The probability of getting at most 4 heads in five coin tosses can be found by adding the probabilities of getting 0 heads, 1 head, 2 heads, 3 heads, and 4 heads.
The probability of getting 0 heads is 1/32.The probability of getting 1 head is 5 * (1/2)^4 * (1/2) = 5/32.The probability of getting 2 heads is 10 * (1/2)^3 * (1/2)^2 = 5/16.The probability of getting 3 heads is 10 * (1/2)^2 * (1/2)^3 = 5/16.The probability of getting 4 heads is 5 * (1/2)^1 * (1/2)^4 = 5/32.So, the total probability of getting at most 4 heads is (1/32) + (5/32) + (5/16) + (5/16) + (5/32) = 1.