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

the probability that she threw 1,2,3,4 is 1/2
plse mark it the brainliest

Answer 2

Answer:

= $\frac{8}{11}$

Step-by-step explanation:

Consider the following events:

  E₁ = Getting 5 or 6 in a single throw a die.

  E₂ = Getting 1,2,3 or 4 in a single throw of a die

  E₃ = Getting exactly one head

We have, P(E₁) = $\frac{2}{6}$ = $\frac{1}{3}$

                P(E₂) = $\frac{4}{6}$ = $\frac{2}{3}$

P (A / E₁) = Probability of getting exactly one head when a coin is tossed three times.

      = ³C₁ ($\frac{1}{2}$)¹ ($\frac{1}{2}$)²

     = $\frac{3}{8}$

P (A / E₁) = Probability of getting exactly one head when a coin is tossed only once = $\frac{1}{2}$

                    = P (E₂) P (A/E₂) / P(E₁) P (A/E₁) + P(E₂)P(A/E₂)

                    = 2/3 × 1/2 / 1/3 × 3/8 + 1/2 × 2/3

                    = 1/3 / 1/8 + 1/3

                    = 1/3 × 24/11

 FINAL RESULT = $\frac{8}{11}$

GOOD LUCK !!