Question

Munna enjoys flying his kite. On any given day, the probability that there is a good mited is \( \frac{3}{4} \). If there is a good wind, the probability that the kite will fly is \( \frac{5}{8} \). If there is note good wind, the probability that the kite will fly is \( \frac{1}{16} \). Further, if the kite flies, probability that it sticks in a tree is \( \frac{1}{2} \). Draw a probability tree diagram for this and hence calculate the following probabilities : 

(i) that there is a good wind and the kite flies.

(ii) that whatever the wind, the kite does not fly. 

(iii) that whatever the wind, the kite sticks in a tree.

Answer 1

Let E₁ = There is a good wind

E₂ = There is not a good wind

A = kite flies

B = kite sticks in a tree

\(\therefore\) P(E₁)  = 3/4, P(E₂) = 1/4

P(A/E₁) = 5/8

P(A/E₂) = 1/16

P(B/A) = 1/2

(i) Probability that there is a good wind and kite flies

= P(A \(\cap\) E₁) = P(A/E₁) P(E₁) = 5/8

= 5/8 x 3/4 = 15/32

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

 = 5/8 x 3/4 + 1/16 x 1/4

 = 15/32 x 1/64 = 31/64

Probability that kite does not fly

 = P(\(\bar A\)) = 1 - P(A) = 1 - 31/64 = 33/64

(iii) If kite does not fly then it can not sticks in the tree.

\(\therefore\) P(B/A^c) = 0.

Now, P(B) = P(B/A) P(A) + P(B/A^c)P(A^c)

 = 1/2 x 31/64 + 0 x 33/64

 = 31/128