Question

Two different coins are tossed simultaneously. What is the probability of getting:

1. at least one head?
2. at most one tail?
3. a head and a tail?

Answer 1

A coin has two faces Head and Tail.

∴ Two coins are tossed, which are HH, HT, TH, and TT.

S = {(H, H), (H, T), (T, H), (T, T)}

∴ n(S) = 4

(i) A is an event (getting at least one head)

∴ A = {(H, T), (T, H), (H, H)} or n(A) = 3

Thus, the probability of getting at least one head

= `(n(A))/(n(S))`

= `3/4`

(ii) Now, Outcomes with at most with 1 tail = HH, HT, TH

Thus, P(getting at most 1 tail) = `"Number of outcomes with almost 1 tail"/"Total number of outcomes"`

= `3/4`

(iii) Let A be the event of getting one head and one tail, and let B be the event of getting at most two tails.

A = {HT, TH}

n(A) = 2

B = {HH, HT, TH, TT}

n(B) = 4

P(getting one head and one tail):

= P(A) = `(n(A))/(n(S))`

= `2/4`

= `1/2`