Question

If a coin is tossed twice, then the events 'occurrence of one head', 'occurrence of $2$ heads' and 'occurrence of no head' are -

• A. Independent
• B. Equally likely
• C. Not equally likely
• D. Both (A) and (B)

Answer 1

Answer: (C)

Not equally likely

Possible outcomes when a coin is tossed $=$ H or T

Possible outcomes when a coin is tossed twice$=$ HH,TT,TH,HT

$=4$ outcomes

P(occurrence of $1H$) $=$ TH,HT

$=2/4=1/2$

P(occurrence of $2H$) $=$ HH

$=1/4$

P(occurrence of no H) $=$ TT

$=1/4$

Therefore, the probability of occurrence of no head and occurrence of no head and occurrence of two head is same but probability of occurrence of one Head is $1/2$. Thus the events are:-

Not equally likely.