A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Question

A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
Or

From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30 � and 45 � respectively. Find the distance between the cars.

Philoid · Accepted Answer

The possible outcomes on tossing a coin 3 times are,

S = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT] = 8

Out comes when Hanif wins = [HHH, TTT] = 2

∴ P (Hanif wins) =

P(Hanif win) + P(Hanif lose)=1

+ P(Hanif lose)=1

∴ P (Hanif will lose) = 1 - 3/4= 1/4

Or

The figure demonstrates the condition given in the question.

We have to find the distance between D and C.

In Δ ABD,

( tan θ = Height/Base)

BD =100√3 m

In Δ ABC,

( tan θ = Height/Base)

BC=100 m

CD=DB + BC=100√3 + 100 =100(√3 + 1)
=100(1.73 + 1) =100(2.73) =273m

∴ CD=273m