Question

Q1. Determine P: A coin is tossed three times.
(i) E: heads on the third toss, F: heads on first two tosses.
(ii) E: at least two heads, F: at most two heads.
(iii) E: at most two tails, F: at least one tail.

Answer 1

One coin is tossed three times then the sample space for this will be:

HHH , HHT , HTH, THH

TTT , TTH , THT , HTT

(i)

E = heads on the third toss

So, E = 4

Total outcomes = 8

So, P(E) = E / 8

☛ P(E) = 4/8

☛ P(E) = 1/2

Also,

F = heads on the first two tosses

So, F = 2

Total outcomes = 8

Now, P(E) = F/8

☛ 2 / 8

☛ P(E) = 1/4

(ii)

E = atleast two heads

So, E = 4

Total Outcomes = 8

Now, P(E) = E/8

☛ P(E) = 4/8

☛ P(E) = 1/2

Also,

F = at most two heads

So, F = 7

Total outcomes = 8

Now, P(E) = F/8

☛ P(E) = 7/8

(iii)

E = at most two tails

So, E = 7

Total outcomes = 8

Now, P(E) = E/8

☛ P(E) = 7/8

Also,

F = atleast one tail

So, F = 7

Total outcomes = 8

Now, P(E) = F/8

☛ P(E) = 7/8