Question

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 1

Use value E₁ = 5 or 6 to get

E₂ = getting 1, 2, 3, or 4

n(E₁) = 2, n(E₂) = 4 n(s) = 6

P(E₁) = `2/6 = 1/3`

P(E₂) = `4/6 = 2/3`

Let E = one head is obtained

P(heads are obtained when the coin is tossed 3 times) = P(E|E₁)

= P(HTT, THT, TTH)

= `3/8`

P(heads appear when the coin is tossed 1 time) = P(E|E₂)

= `1/2`

Required process = `(1/2 xx 2/3)/((1/2 xx 2/3) + (3/8 xx 1/3))`

= `8/8 + 3`

= `8/11`