Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1,2,3 or 4 with the die?

Answer

N/a

Explanation

Let `E_(1)=` event of getting 5 or 6 on die,
`E_(2)=` event of getting 1,2,3 or 4 on die
and `E=` event of getting head on die.
Now, `P(E_(1))=` probability of getting 5 or 6 on die
`=2/6=1/3`
`P(E_(2))=` probability of getting 1,2,3 or 4 on die
`=4/6=2/3`
`P(E//E_(1))=` probability of getting one head in three tosses of a coin `=3/8`
`P(E//E_(2))=` probability of getting one head in one toss of a coin `=1/2`
Now required probability
`P(E_(2)//E)=(P(E_(2)).P(E//E_(2)))/(P(E_(1)).P(E//E_(1))+(E_(2)).P(E//E_(2)))`
`=(2/3xx1/2)/(1/3xx3/5+2/3xx1/2)`
`=(2//6)/(3/24+2/6)=2/6xx24/11=8/11`