Two unbiased coins are tossed simultaneously. Find the probability of

1.	Two unbiased coins are tossed simultaneously. Find the probability of getting(i) two heads (ii) at least one head (iii) at most one head.
Answer» If two unbiased coins are tossed simultaneously, we obtain any one of the following as an out come : HH, HT, TH, TT So, Total number of elementary events = 4 (i) Two heads are obtained if elementary event HH occurs. So, Favorable number of events = 1 Hence, P (Two heads) =1/4 (ii) At least one head is obtained if any one of the following elementary events happen: HH, HT, TH So, favorable number of events = 3 Hence P (At least one head) =4/6=2/3 (iii) If one of the elementary events HT, TH, TT occurs, than at most one head is obtained So, favorable number of events = 3 Hence, P (At most one head) =3/6=1/2

Two unbiased coins are tossed simultaneously. Find the probability of getting(i) two heads (ii) at least one head (iii) at most one head.

Answer»

If two unbiased coins are tossed simultaneously, we obtain any one of the following as an out come :

HH, HT, TH, TT

So, Total number of elementary events = 4

(i) Two heads are obtained if elementary event HH occurs.

So, Favorable number of events = 1

Hence, P (Two heads) =1/4

(ii) At least one head is obtained if any one of the following elementary events happen: HH, HT, TH

So, favorable number of events = 3

Hence P (At least one head) =4/6=2/3

(iii) If one of the elementary events HT, TH, TT occurs, than at most one head is obtained

So, favorable number of events = 3

Hence, P (At most one head) =3/6=1/2

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